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What is Combustion?

Combustion is a chemical process in which a substance reacts with oxygen and generates heat in the process.

Combustible substances are those substances that undergo combustion. It means that these substances give off heat and sometimes light (as a flame or glow) when they react with oxygen.

Inflammable substances are substances which have low ignition temperature and catch fire easily. They burn with a flame. For example, petrol, LPG etc.

Why do we say that food is fuel for our body?

When we eat food, it gets broken down in simpler substances which react with oxygen and generate energy (or heat). Hence, food is referred to as ‘fuel’ for our body.

Conditions necessary for the Combustion to take place are:

1. Combustion requires fuel.

Combustion only takes place when there is a fuel which produces heat and light when it catches fire. For example, petrol and diesel.

1. Combustion requires air.

We can prove it with the help of the following experiment:

A candle keeps burning in open air. However, when we cover it with a glass or a jar, it only burns until the oxygen inside it is consumed. Once the oxygen is exhausted, the flame of the candle flickers off.

1. Combustion requires heat.

The substance must reach its ignition temperature to catch fire.

Ignition temperature is the lowest temperature at which a substance catches fire or starts burning.

Types of Combustion

• Rapid Combustion: Combustion in which a gas burns quickly producing heat and light in the process. E.g. LPG
• Spontaneous Combustion: Combustion in which a material bursts into flames suddenly without applying heat. E.g. Phosphorus which burns at room temperature.Spontaneous combustion of coal dust often causes accidental fires in coal mines. Heat from the sun or lighting may also cause spontaneous forest fires.
• Explosion: When a material bursts suddenly to produce heat, light and sound on the application of heat or pressure, it is called an explosion. E.g. Crackers and fireworks which release a large amount of gas too.

How do We Control Fire?

We can control the fire by one or more of the following:

• Removing the fuel
• Cutting off the air supply (or oxygen supply)
• Cutting off heat or lowering the temperature of the fuel

How do fire extinguishers work?

Fire extinguishers are devices used to put out fires. They either cut off the air supply to fire or cool off the fuel (below the ignition temperature) or both. The three main types of fire extinguishers are:

1. ‘Dry Powder’ Fire Extinguisher: This type of fire extinguishers contain a mixture of baking soda (sodium bicarbonate) and sand. When you throw it over the fire, the baking soda decomposes by its heat to produce carbon dioxide. Since CO₂ is heavier than air, it descends to envelop the burning flame and cuts off its contact with air (and the oxygen supply).

2NaHCO₃  → Na₂CO₃ + H₂O + CO₂

1. ‘Soda-acid’ Fire Extinguisher: This fire extinguisher is a metallic cylinder which contains the sodium bicarbonate (NaHCO₃) solution. At the bottom of the cylinder, the concentrated sulphuric acid (H₂SO₄) is placed in a thin sealed glass tube. A fixed wire gauze surrounds this tube.

Below the tube, a plunger is placed with its sharp end touching the thin glass tube.

On the top of the cylinder, there is a nozzle which is sealed with wax.

When the plunger hits against the floor, its sharp end breaks the thin glass tube and the acid inside it reacts with sodium bicarbonate to produce carbon dioxide. CO₂ forces the wax seal open and rushes out of the nozzle to put out the fire in the direction where the nozzle is pointed.

1. ‘Foam-type’ Fire Extinguisher: Like the soda-acid fire extinguisher, it uses sodium bicarbonate solution. However, in this case, a substance called Saporin or Turkey Red Oil is added to the solution to produce foam along with the gas from the nozzle. Since this foam is lighter than oil, it floats on the surface of the oil and cuts off its air supply. Hence, it is very effective in putting out oil fires.

When should we use (or not use) water to extinguish the fire?

When wood, paper and clothes are on fire, we can use water to extinguish them. Water lowers the temperature of burning material below ignition temperature and thus, the fire stops burning.

We should not use water when electrical equipment is on fire as water may conduct electricity and give a shock to people dousing the fire. Also, it should not be used when oil or petrol catches fire as water is lighter than oil and petrol and sinks down. Oil and petrol keep floating on the top and keep burning.

What should we do when electrical equipment or inflammable materials (like petrol) catch fire?

Carbon Dioxide is the best fire extinguisher in such cases. CO₂ is heavier than oxygen and hence, covers the burning material like a blanket and cuts off its oxygen supply. Also, it does not harm the electrical equipment.

CO₂ can be stored as a liquid in cylinders at high pressure. When it is released, it immediately expands, cools down, and envelopes the fire – bringing down the temperature of the fuel. One can also pour dry chemicals like sodium bicarbonate (or baking soda) or potassium carbonate on the fire as they release CO₂ near a fire.

Flame

Flame is a hot glowing body of ignited gas which is produced when something is on fire.

Some materials burn with a flame and some do not. Here is a table based on a general observation:

Materials forming Flame on Burning

Material	Forms flame	Does not form a flame
Candle	Forms flame
Magnesium		Does not form a flame
Camphor	Forms flame
Kerosene Stove	Forms flame
Charcoal	Forms flame

Structure of a Flame

A flame has three zones:

1. Outermost zone is blue in colour and is the hottest part of the flame. This is also the zone where complete combustion takes place.
2. Middle zone is yellow in colour and is moderately hot. In this zone, partial combustion takes place.
3. Innermost zone is black in colour and least hot. Here, we can find the unburned wax vapours of a candle.

Note: Kerosene oil and molten wax vapourise during burning but charcoal does not produce flame or vapourise when it burns.

Why do goldsmiths blow at the outermost zone of a flame for melting gold and silver?

The outermost zone of a flame is its hottest part. Gold and silver have high melting points and hence, goldsmiths blow at the outermost zone of the flame to melt gold and silver quickly.

What is a Fuel?

Fuels are substances that give us heat which we use for domestic and industrial purposes, such as wood, kerosene, and petrol.

What will an ideal fuel or good fuel look like?

Ideally, a good fuel is one which:

• has proper ignition temperature (neither too high nor too low),
• does not produce undesirable or poisonous substances and cause pollution,
• does not leave behind much ash,
• is cheap,
• is readily available,
• produces a large amount of heat or have high calorific value,
• has a moderate rate of consumption,
• is easily controllable (can be started or stopped as needed),
• is easy to handle and transport, and
• has low moisture content (so that it burns easily).

Note: Some fuels are cheaper than others.

Fuel Efficiency

Fuel efficiency of a fuel depends on its calorific value.

The calorific value of a fuel depends on the amount of heat produced by complete combustion of 1 kg of the fuel. The unit used to measure the calorific value of a fuel is kilojoule per kg (kJ/kg).

Calorific Value of Common Fuels We Use

If we look at the table, we will see that hydrogen seems to be the most efficient fuel followed by LPG. CNG and Methane come next, closely followed by Kerosene, Diesel and Methane. Cow dung cake seems to be the least efficient fuel here.

Uses of Fuels

Some of the ways in which common fuels are used are:

1. Gasoline is used in cars, scooters and other vehicles we use every day.
2. Natural gas is used in heating systems, water heaters, dryers, and stovetops in our homes.
3. Oil and natural gas are used in making several things that we use every day. Hydrocarbons, for example, are used in making plastics, pharmaceuticals and several other items we use daily.
4. Coal is the primary fossil fuel used in many thermal power plants to produce electricity.

Types of Fuels

Fuels can mainly be divided into three groups:

• Liquid Fuels: Petroleum (which is a fossil fuel), crude oil (from which we get petrol or gasoline), diesel, kerosene oil etc.
• Solid Fuels: Firewood, charcoal, coal (fossil fuel which is mined as steam coke or soft coke), dung cakes, tallow (animal fat), straw and other agricultural wastes, paraffin wax, camphor etc.
• Gaseous Fuels: Most commonly used gas is LPG (Liquid Petroleum Gas) which we use as cooking gas at home. Some of the other commonly used gaseous fuels are:
  • We get CNG (Compressed Natural Gas) from natural oil wells.
  • Natural gas (or methane) gets released from the putrefying organic matter.
  • Butane gas is obtained from natural gas.
  • In the villages, animal dung and farm waste are used to produce biogas. Biogas is also collected from sewage plants.
  • When hard coke is heated and converted into coke, coal gas is produced.
  • Water gas is produced by passing steam over red-hot coke.
  • Acetylene used a gas produced by adding calcium carbide to water. Its smell is a bit unpleasant but the flame it produces is so hot that it is used for cutting metals and welding purposes.

Harmful Effects of Burning Fuels

1. Carbon fuels like wood, coal and petroleum release ash and fine unburnt carbon particles in the air which can cause respiratory diseases like asthma. These fine particles are referred to as Suspended Particulate Matter (SPM).
2. Incomplete combustion of fuels (such as coal, gasoline and other fossil fuels) releases carbon monoxide gas which is very poisonous and can kill people sleeping in the room where coal is burning. CO combines with haemoglobin in our blood to form carboxyhemoglobin and renders it incapable of transporting oxygen. These fuels also release unburnt hydrocarbons, many of which are carcinogenic (cause cancer) and pose serious health hazards.
3. Carbon dioxide released by most fuels during combustion is causing an imbalance in the atmosphere. Deforestation is also leading to a situation where there are fewer trees to absorb the carbon dioxide. This is leading to global warming.
4. Burning of coal and diesel releases sulphur dioxide gas which is corrosive in nature and causes irritation in nose, throat and airways. It also causes shortness of breath, wheezing, and a feeling of tightness around the chest. Petrol engines release gaseous oxides of nitrogen. These sulphur and nitrogen oxides dissolve in rainwater to form acids and cause acid rain.

Global warming is the rising temperature of the Earth’s atmosphere which is causing the melting down of glaciers making the sea levels rise and causing floods in coastal areas. It is caused due to the elevated levels of carbon dioxide in the atmosphere as CO2 absorbs infrared radiation emitted by the Earth and radiate it back to the atmosphere and raise its temperature. This is also known as the ‘greenhouse effect’.Acid Rain refers to the rain of acids that is very harmful to crops, soil, animals, and buildings. These acids are formed when sulphur and nitrogen oxides dissolve in rainwater. Acid rains also damage trees at high elevation (such as red spruce that grows 2,000 ft above sea level), causes acidification of lake or stream water, and damage forest soils. Irreplaceable buildings, statues and sculptures which are part of a nation’s cultural heritage can get destroyed due to acid rain.

Why do we not burn wood anymore?

Wood is a low-cost fuel and is easily available but burning it releases a lot of smoke which causes respiratory problems. Moreover, cutting of trees for wood (as fuel) also leads to deforestation. Hence, people now prefer to use coal or LPG as fuel instead.

Why should we use CNG as automobile fuels?

CNG is a cleaner fuel and causes much less pollution than petrol and diesel. Hence, we should use CNG-powered vehicles now.

How to Conserve Fuels?

To conserve fuels, we should:

• Collect all material required while cooking at one place before switching on the gas,
• Check the pressure of tyres regularly,
• Choose walking over using cars or motorbikes for short distances, and
• Use public transportation for travelling instead of private vehicles.

Introduction

→ There are two types of resources:
(i) Inexhaustible Natural Resources (Renewable sources of energy)
(ii) Exhaustible Natural Resources (Non-renewable sources of energy)

Inexhaustible Natural Resources

→ They are renewable sources of energy that are replenished at a rate faster than that at which they are consumed.

→ These resources are present in unlimited quantity in nature and are not likely to be exhausted by human activities.

Examples:

→ Tidal energy, wave energy, ocean thermal energy.

→ Solar energy: Solar cooker, solar water heater (very efficient for small scale electricity production)

→ Geothermal energy: Heat energy inside the earth

→ Nuclear energy: Not dependent on solar energy, never-ending source, very efficient source, more environment friendly.

Exhaustible Natural Resources

They are non-renewable sources of energy are those that are consumed at a rate faster than that at
which they are replenished. The amount of these resources in nature is limited which can be exhausted by human activities.

Examples:

→ Forests, wildlife, minerals, coal, petroleum, natural gas etc.

→ Fossil fuels: Coal, petroleum and natural gas
Advantages of using fossils fuels:
Easy availability
Generate heat that is easily converted into electricity.

→ Coal, petroleum, and natural gas were formed from the dead remains of living organisms. Hence, they are known as fossil fuels

→ Resources such as coal and petroleum are limited. Burning of such fuels is the major cause of air pollution. Therefore, these fuels should be used only when necessary.

→ Burning of fossil fuels releases gases like carbon dioxide which cause greenhouse effect.

Coal

→ It is a fossil fuels which is hard solid and black in colour.

• Story of Coal

→ Due to natural processes, the dense forests got buried under the soil.

→ Under high temperature and high pressure, dead plants got slowly converted to coal.

→ The slow process of conversion of dead vegetation into coal is called carbonisation.

• Uses of Coal

→ It is used as fuel to cook food. Earlier, it was used in railway engines to produce steam.

→ It is used in thermal power stations to generate electricity.

→ Coke, coal tar, and coal gas are the products of coal.

Products from coal

Coke

→ It is a tough, porous and black substance.

→ It is the pure form of carbon and is used in the extraction of steel and many other metals.

Coal tar

→ It is black, thick liquid with unpleasant smell.

→ It is the mixture of about 200 substances.

→ The products obtained from coal tar are used as starting materials for dyes, drugs, paints, perfumes, etc.

Coal gas

→ It is obtained during the processing of coal to obtain coke.

→ It is used as a fuel in many industries situated near the coal processing plants.

Petroleum

→ Petroleum was formed from the dead organisms present in the sea.

→ Petrol, diesel, kerosene, paraffin wax, lubricating oil, and petroleum gas are the products of petroleum.

→ The process of separating various constituents of petroleum is known as refining.

→ Refining of petroleum is done in fractionating column.

→ Components with higher boiling points are collected at the bottom of the fractionating column.

→ Components with lower boiling points are collected at the top of the column.

Petroleum and its uses

Constituents of Petroleum	Uses
Petroleum Gas in Liquid form (LPG)	Fuel for home and industry.
Petrol	Motor fuel, aviation fuel, solvent for dry cleaning
Paraffin wax	Candle, Vaseline, Ointments etc.
Diesel	Fuel for heavy motor vehicles, electric generators
Kerosene	Fuel for stoves, lamps.
Lubricating oil	Lubrication.
Bitumen	Paints, road surfacing

→ Complete combustion of hydrocarbons lead to formation of carbon dioxide and water, while incomplete combustion of hydrocarbons yield carbon monoxide and water.

→ Carbon dioxide as well as carbon monoxide are responsible for pollution in our environment.

→ The test used to determine the amount of carbon monoxide in vehicle’s exhaust gases is known as emission test.

→ Gas analyzer is used in detection of carbon monoxide in exhaust gases.

→ Petroleum is a natural resource

→ The formation of petroleum takes place over a period of millions of years.

→ Petroleum reserves are limited i.e. they are found only in a few places on the Earth.

→ The ever increasing population has further increased the demand for petroleum and its products.

→ In India, the Petroleum Conservation Research Association (PCRA) advises people on the various methods that can be adopted to conserve petrol/diesel.

Cracking

→ Heating higher alkanes to sufficiently high temperatures in absence of oxygen, in order to obtain lower hydrocarbons is known as cracking or pyrolysis.

Natural Gas

→ Natural gas is formed from dead organisms which decompose in the absence of air under conditions of high pressure and temperature.

→ It is stored under high pressure as compressed natural gas (CNG). It is used as a fuel for vehicles because it is a cleaner fuel (less polluting).

Introduction

→ Materials are classified in two types i.e. metals and non-metals.

→ Metals can be distinguished from non-metals on the basis of their physical and chemical properties.

Metals

Physical properties of metals

→ They have shining surface in their pure state. It is also called metallic lustre.

→ They are generally hard. The hardness varies from metal to metal.

→ Metals are malleable. This means it can be made thin sheets by beating.

→ Ductile which means it can be drawn into thin wires. As an example, Gold is highly ductile metal.

→  The are good conductors of heat and have high melting point.

→ The conduct electricity.

→ Most of metals are sonorous which means it can produce sound.

Chemical Properties of metals

→ Metals combine with oxygen to form metal oxides.
2Cu + O₂ → 2CuO
4Al + 3O₂ → 2Al₂O₃

→ Most metal oxides are insoluble in water.
If metal oxides are soluble, they form alkali.
Na₂O + H₂O → 2NaOH
K₂O + H₂O → 2KOH

→ Sodium, potassium react very easily with O₂. So, they are kept immersed in kerosene.

→ Mg, Al, Zn, Pb form thin layers of oxides when kept in open.

Reaction of metals with water

→ Metals produce metal oxide + H₂ on reaction with water.
If oxide is soluble, then metal hydroxide is formed.

→ Magnesium doesn’t react with cold water.

→ Al, Zn, Fe do not react with H₂O, but react with steam.
2Al + 3H₂O → Al₂O₃ + 3H₂
3Fe + 4H₂O → Fe₃O₄ + 4H₂

Non-metals

Physical properties of non-metals

→ Non-metals are found in all the three states i.e. solid, liquid and gas, at room temperature.

→ Iodine (non-metal) has lustre.

→ Carbon has allotropes which means it exists in different forms.

→ Diamond is hard and Graphite conducts electricity.

Difference between Metals and Non-metals

Metals	Non-metals
Generally, these are hard and lustrous.	These are soft and have no lustre.
These are malleable and ductile.	These are non-malleable and non-ductile
These are sonorous (produce ringing sound when struck).	These are not sonorous.
These are good conductors of heat and electricity.	These are poor conductors of heat and electricity.
These react with oxygen to produce metal oxides, which are basic in nature.	These react with oxygen to form non-metallic oxides, which are acidic in nature.
These react with acids to produce metal salts and hydrogen gas.	These do not react with acids.
Some metals react with bases to produce hydrogen gas.	Reactions of non-metals with bases are complex.

Reaction with Acids

→ Metal + Dilute acid → Metal salt + H₂

→ H₂ doesn’t evolve in the case of HNO₃ as it is a strong oxidising agent. It oxidises H₂.

→ Cu does not react with acids like dilute H₂SO₄ and dilute HCl.

• Aqua regia

→ Freshly-prepared concentrated HCl and concentrated HNO₃ in 3:1 ratio

→ It can dissolve even gold and platinum.

Reaction with Bases

→ Metals react with bases to produce hydrogen gas.

→ Reactions of non-metals with bases are complex.

Uses of metals

→ In making machinery, automobiles, jewellery, trains, aeroplanes, cooking utensils, etc.

→ Gold is used for making jewellery, wires, and coins and in dentistry.

→ Silver is used for making coins, ornaments, very thin wires, table cutlery and in photographic films.

→ Copper is used for making wires, utensils, statues, alloys and coins.

→ Iron is used for construction of ships, buildings, automobiles and railway bridges etc.

→ Tin is used for tinning food cans, and making alloys.

→ Lead is used for making batteries, and alloys.

→ Zinc is used in prevention of rusting, making brass and bronze and in dry cells.

→ Aluminium is used in making wires, foils, and alloys.

→ Mercury is used for making amalgams and in thermometers.
→ Magnesium is used for making fire works, and alloys.

Uses of non-metals

→ They are used in fertilizers, in water purification process, crackers, etc. Oxygen, a non-metal, is essential for our life as all living beings inhale it during breathing.

→ Nitrogen dilutes the activity of oxygen in air. It is used by plants to manufacture proteins.

→ Oxygen is essential for respiration and combustion of fuels.

→ Chlorine is used for bleaching fabrics, sterilization of drinking water, and in manufacturing insecticides and pesticides.

→ Iodine is essential for proper functioning of human body, and in photographic films.

→ Graphite is used as pencil lead, dry lubricant, in electrolytic cells and nuclear reactors.

→ Helium is a noble gas which is used in weather observation balloons.

→ Argon is a noble gas which is used for filling electric bulbs.

Types of Reactions

• Displacement reactions

In this reactions, a more reactive metal displaces a less reactive metal from their compounds in aqueous solutions. (However, a less reactive metal cannot displace a more reactive metal.)
Example:
CuSO₄ (Blue) + Zn → ZnSO₄ (Colourless) + Cu (Red)
(Copper Sulphate + Zinc → Zinc Sulphate + Copper)

Pb + CuCl₂ → PbCl₂ + Cu

• Double displacement reaction

In this reaction, exchange of ions occurs between two compounds.

Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl

Alloys

→ Alloys are homogeneous mixtures of two or more metals (or metal and non-metal). Alloying is done to enhance the properties of metals.

→ Alloys of aluminium are also useful as they are both light and strong. Some of its alloys are duralumin, magnelium, etc.

→ Some alloys of iron are steel, stainless steel, etc. Steel is an alloy of iron and carbon.

→ Some alloys of zinc are brass, bronze, and German silver.

→ On the basis of composition, alloys are of two types: Substitutional alloys in which atoms of one element randomly replace the atoms of another metal. And interstitial alloys in which small atoms like hydrogen, boron, carbon and nitrogen occupy the holes in the crystal structure of the metal.

• On the basis of constituent elements, alloys are of two types:
→ Ferrous alloys: They contain iron as base metal. Example: steel, alnico etc.
→ Non ferrous alloys: They do not contain iron as base metal. Example: brass, bronze, duralumin etc.

Fabrics are made by weaving fibres (or threads) obtained from natural or artificial sources. They can be of two types:

What are Synthetic Fibres?

What is a synthetic fibre made up of?

A synthetic fibre, as well as plastic, is made up of a chain of small units (called Monomers) which combine to form polymers.

Monomers: A monomer is a single molecule that can bond with other identical molecules to form polymers through a process called Polymerization.

Polymers: Polymer is a Greek word in which ‘poly’ means ‘many’ and ‘mer’ means units. Hence, polymers are large molecule made up of several molecules (or monomers) linked together.

Example of Polymers:

• All synthetic fibres, such as Rayon and Nylon, are polymers.
• Polymers are also found in Nature. ‘Cotton’ is a polymer called ‘Cellulose’. ‘Cellulose’ is made up of a number of single units (or monomers) called ‘Glucose’.

Polymerization Reaction: The process of linking small monomers together to form polymers is called Polymerization.

Types of Synthetic Fibres 

Rayon

Rayon is a versatile fibre and can imitate the feel and texture of silk, wool, cotton and linen with drape and slipperiness akin to nylon.

Why Rayon is called artificial silk?

Rayon resembles silk in appearance, texture and shine. Hence, it is also known as Artificial Silk.

Silk fibre was discovered in China and made from silkworms. It had a beautiful texture and was very costly. By the end of the 19^th century, scientists managed to make an artificial silk-like fibre made by treating wood pulp chemically.

Uses of Rayon

This man-made fibre uses natural material (wood pulp) and can be woven like silk fibre. It is cheaper than silk and can be dyed in a variety of colours. It can be:

• Make apparels like suits, slacks, jackets etc.
• Make automobile tyre cords (because of its strength)
• Mixed with cotton to make bedsheets and bedspreads
• Mixed with wool to make carpets and blankets
• Used to make other home furnishings, such as curtains and tablecloths

Nylon

Nylon is the first synthetic fibre to be prepared without using any natural raw materials (materials produced by plants and animals).

Which properties make Nylon suitable for:

Making Ropes used for Rock Climbing: Strong fibre, Lightweight, Weather Resistant

Making Fishing Nets: Strong, Elastic, Water Resistant

Making Tents: Strong, Light, Does Not Absorb Much Water, Dries Quickly

Uses of Nylon

Developed in 1931, this thermoplastic silky material is strong, elastic, light, lustrous and easy to wash. A nylon thread is, in fact, stronger than a steel wire. Hence, it is used to:

• Make clothes (including socks)
• Make parachutes as well as ropes for rock climbing
• Make ropes, toothbrushes, and car seat belts etc.
• Make tents, curtains, and sleeping bags

Polyester

Polyester fibre does not get wrinkled easily. Hence, a fabric made from this fibre is easy to wash and does not need to be ironed – which makes it suitable for dress material.

Polyester is made up of two words – ‘poly’ which means many, and ‘ester’ which is a chemical.

Esters are chemicals which give fruits their smell.

Name some types of Polyester fibres.

Some popular polyester fibres are:

• Terylene (often known by brand name Dacron) which can be drawn into a very fine fibre and can be woven like any other yarn.
• Polyethylene terephthalate (P.E.T.) is used for making wires, films, bottles, utensils and other products.

What are blended fibres? Give some examples.

Blended fibres are formed by mixing natural and synthetic fibres. Polyester is often used in blended fibres. For Example,

• Polywool is made by mixing polyester and wool.
• Polycot is made my mixing polyester and cotton.
• Terrycot is made by mixing Terylene and cotton.

Uses of Polyester

Since polyester is strong, wrinkle-resistant and water-resistant, it has several uses. It can be used to:

• Make a variety of textiles (including sarees, curtains, dress materials etc.) and can be blended with natural fibres (like cotton and wool)
• Make films, magnetic recording tapes, etc (as Mylar)
• Make sails of sailboats
• Make water hoses for firefighting purposes

Acrylic

Acrylic is a strong, lightweight and warm synthetic fibre that resembles wool. It is available in a number of colours and is more durable and affordable than natural wool.

Acrylic fibre, fabric, plastic or paint are all made from acrylic acid. The word ‘acrylic‘ means ‘containing acryl (or acrolein)‘ Acrolein is the sharp and bitter liquid in onions and has its roots in two Latin words – ‘acer’ which means ‘sharp’, and ‘olere’ which means ‘to smell’.

Why storage of acrylic clothes is easier than woollen clothes?

Woollen clothes need naphthalene balls to protect them from attack by insects. Acrylic is synthetic wool and is hence, resistant to the action of moths and insects.

Uses of Acrylic Fibre

Acrylic can mimic wool as well as cotton at times and is hypoallergenic in nature. It means that people who have sensitive skin can wear it easily. Some acrylic fibres are very resilient – more than other natural or synthetic fibres. It can be used to:

• Make woollen clothes like hats, scarves, gloves, sweaters, blankets, and other home-furnishing fabrics.
• Make fake fur used for making toys and fur accessories.
• Make garments for babies (as the fabric is machine-washable).

Characteristics of Synthetic Fibres

What are synthetic fibres made up of?

All the synthetic fibres are manufactured by processing raw materials of petroleum origin in a number of ways. The raw materials of petroleum origin are called Petrochemicals.

Why should we not wear synthetic clothes in the kitchen?

Synthetic fibres melt on heating. If the clothes catch fire, the fabric made up of synthetic fibres will melt and stick to one’s body. Hence, it is recommended that one should not wear synthetic clothes while working in the kitchen or laboratory.

Plastics

Plastic is a polymer (like the synthetic fibre) which can be moulded into different shapes. The word ‘plastic’ originates from the Greek word ‘plastikos’ which means ‘that can be moulded or shaped’. Plastic polymers can have different types of arrangement of monomers:

Plastic can be recycled and used. It can also be melted, rolled into sheets, made into wires, and coloured.

Some popular types of plastics are:

Plastics as Materials of Choice

Advantages of Plastic
Lightweight	Lower price	Good strength	Easy handling	Not-reactive(does not rust like iron when exposed to water and air, and doesnot corrode easily)	Poor conductor of heat and electricity

Give Reasons Why:

Buckets are made of plastic these days.

Plastic buckets are strong, lightweight, and do not rust.

Bakelite plastic is used to make electrical switches.

Bakelite is a poor conductor of heat and electricity. Hence, they would not give anyone an electric shock when someone touches the switch.

Melamine is used to make crockery.

Melamine is unbreakable, fire resistant, and tolerates heat better than plastics. Hence, it can be used to make crockery that can hold hot liquids or dishes served in it.

Plastics are used in cars, aircraft and spacecraft.

Plastics are strong, durable, lightweight, and corrosion-resistant.

Chemicals are stored in plastic bottles.

Plastic bottles are lightweight, unbreakable, corrosion-resistant, and are resistant to the action of chemicals. Hence, they are suitable for storing chemicals.

Which plastic is used to make:

Non-stick coating on Cookware: Teflon

Insulation covering on Wires: PVC

Polythene Bags: Polythene

Flame-resistant Uniforms: Melamine

Special uses of Plastic

Besides being used in packaging for food and non-food items and several daily-used items (such as furniture, electrical switches, slippers etc.), plastic also has special uses such as:

• Used in the healthcare industry for packaging of tablets, syringes, doctor’s gloves, a number of medical instruments, and threads for stitching wounds.
• Used to make cookware used in microwave ovens
• Used as a non-stick coating on cookware (made of a special plastic called Teflon is used on which oil and water do not stick)
• Used to make the fire-resistant uniform for firefighters (made of Melamine)

Plastics and the Environment

Plastic is a threat to the environment as it is non-biodegradable. Its disposal is a big problem.

Biodegradable: Material which gets decomposed through natural processes (such as bacterial action) is called Biodegradable.

Non-biodegradable: Material which cannot be easily decomposed by natural processes is called Non-biodegradable.

How do plastics cause environmental pollution?

Plastics cause pollution as they:

• are non-biodegradable, and
• release toxic fumes when burnt (and hence, cause air pollution).

5 Rs to Minimize the Environmental Damage caused by Plastic

Refuse: Do not buy things we do not need.

Reduce: Minimize the use of plastics in our daily lives.

Reuse: Reuse the items we already instead of throwing them away.

Repurpose: If we are not using something, alter or change to use it in a different way.

Recycle: Some plastic waste can be sorted and made into other things in recycling factories. This helps us to reduce our carbon footprint.

How can we minimize pollution caused by plastics at home?

We should use jute, cotton, or paper bags instead of plastics. We also need to minimize the use of plastic in our daily lives (such as using a steel lunch box instead of a plastic one). Also, we should not throw plastics on the road or in the water bodies.

What are Microbes? Microbes or microorganisms are tiny organisms which are so small that we cannot see them with an unaided eye. Some microorganisms can be seen with the help of a magnifying glass (such as fungus that grows on bread) while some can only be seen when you use a microscope (such as bacteria and protozoa). Microorganism were first observed by Anton Van Leeuwenhoek. Viral, Bacterial, and Protozoan Diseases
Causes	Diseases
Viruses	Common Ailments: Cold, Cough, and Influenza (or Flu) Serious Diseases: Polio, Chicken Pox, Measles etc
Bacteria	Typhoid and Tuberculosis (TB) etc
Protozoans	Dysentery and Malaria etc
Table 1: Microbial Diseases

Microorganisms

There are four major types of microorganisms:

Fig 1: Types of Microorganisms

• Bacteria: These are single-celled organisms with a rigid cell wall. They can only be seen under a microscope which enlarges images from 100 to 1000 times.

Fig 2: Ultrastructure of a Bacterial Cell

Types of Bacteria (based on their Shapes) and their Examples

Shape of Bacteria	Example	Image
Comma-shaped Bacteria	Fig 3: Vibrio Cholera	Vibrio Cholerae
Spherical-shaped Bacteria (Cocci)	Fig 3: Streptococcus	Staphylococcus and Streptococcus
Rod-shaped Bacteria (Bacilli)	Fig 4: Salmonella	E.coli and Salmonella
Spiral-shaped Bacteria (Spirilla)	Fig 5: Borrelia	Treponema and Borrelia

Table 2: Shapes of Bacteria (with Examples)

• Fungi: These are non-green plants and hence, cannot make their own food. They either live as parasites (deriving nutrition from host organisms, for example, Puccinia which causes wheat leaf rust) or grow on the organic matter (such as bread mould). 

Fig 7: Puccinia triticina

Fig 8: Bread Mould

Fungi, like mushrooms, moulds, mildews, and years, are eukaryotic. It means that they have a true nucleus.

The  main components of fungi are:

i. Hyphae: They are thread-like filaments which penetrate into substrates, secrete enzymes to break down nutrients into smaller molecules, and absorb them.

ii. Spores are a unit of sexual or asexual reproduction. They can adapt for dispersal and survival for extended periods of time in unfavourable conditions.

• Algae : These are simple plant- like organisms which are usually aquatic in nature. They contain a cell wall and chlorophyll and can make their own food by photosynthesis.Algae can be unicellular or multicellular. Some of the common examples are diatoms, Chlamydomonas, and seaweed.
• Protozoa: Protozoa are unicellular are organisms. Some of them live independently while others live as parasites. Many of the parasitic protozoans cause diseases in plants, domestic animals, and human beings. Example of some protozoans are  Amoeba, Plasmodium and Paramecium

​

Fig 9: Paramecium

How are Viruses different from other microbes?

Viruses are microscopic organisms but they are different from other microbes because they reproduce only inside the cells of the host organism (which can be a plant, animal, or a bacterium).

Fig 10: Types of Viruses

Viruses are much smaller than bacteria and come in a wide variety of shapes and sizes. A complete virus particle is known as Virion.
Virion consists of a nucleic acid surrounded by ‘capsid’. Capsid is a protective coat made of protein. The subunits of this protein called ‘Capsomeres‘. Viruses can be seen only by an electron microscope as they are ultramicroscopic in size.

Outside the body of a living organism, they do not show any reaction and hence, can be crystallized and stored like non-living things.

Where do Microorganisms Live?

Microbes can survive in all kinds of environments – from icy cold climates to hot springs (any kind of temperature); and deserts to marshy lands (any humidity level). Some live independently while others live as parasites – inside the bodies of other organisms (including animals and human beings).

Microorganisms and Us

Some microorganisms are beneficial to us while others are harmful and cause diseases.

How are bacteria useful to us?

Bacteria are helpful because:

• It decomposes organic wastes (such as vegetable peels, animal remains, and faeces etc.).
• It is used in the preparation of medicines.
• It increases soil fertility by fixing nitrogen.
• It is used in the setting of curd and making cheese, pickles, and other food items.

How is yeast useful to us?

Yeast is used in the baking industry (to make bread, pastries, and cakes) because it helps in fermentation. It reproduces rapidly and produces carbon dioxide during respiration. Bubbles of the carbon-dioxide gas it produces fill the spaces in the dough and increases its volume.

It is also used in the commercial production of alcohol and wine which is done by growing yeast on natural sugars present in fruit juices and grains like rice, wheat, and barley.

Antibiotics

What are Antibiotics? What are their uses?

Antibiotics are medicines that can kill or stop the growth of disease-causing microorganisms. For Example, Penicillin.

Antibiotics are used to:

• Cure a variety of diseases (such as streptomycin, erythromycin, and tetracycline that are made from bacteria and fungi),
• Cure microbial infection in animals (by mixing antibiotics with the feed of livestock and poultry), and
• Control several plant diseases.

What precautions should be followed while taking antibiotics and why?

Antibiotics should be taken only on the advice of the doctor, and one must complete the course the doctor prescribes.

Antibiotics taken in wrong doses may make the body resistant to the drug and it may not be effective in the future. Moreover, antibiotics may also kill the beneficial bacteria in the body.

Please Note: Antibiotics cannot cure cold and flu caused by viruses.

Vaccines

Some Definitions to Remember:Pathogens: Disease-causing microbes are called Pathogens. Antibodies: Antibodies are substances our body produces to fight disease-causing microbes. Vaccines: Vaccines are weakened or dead disease-causing microbes that are injected in our body to trigger the production of antibodies. These antibodies remain in the body for a long time to protect it against any attack of disease-causing microbes. Vaccination: The process of protecting the body from pathogens with the help of vaccines is called Vaccination.

Name some of the diseases which can be prevented by vaccines

Some of the diseases that can be prevented by vaccination are:

• Cholera,
• Hepatitis,
• Smallpox, and
• Tuberculosis.

One can get necessary vaccines from nearby hospitals.

How do microbes clean up the environment?

Microbes or microorganisms decompose organic waste and dead remains of plants and animals and convert them into simpler substances (which can again be used by other plants and animals) by the process of biodegradation. Thus, they help us in getting rid of harmful and smelly substances and clean up the environment.

Harmful Microorganisms

Some Definitions to Remember:Communicable Diseases: These are microbial diseases (diseases caused by microbes) that spread from one infected person to a healthy person through air, water, food or physical contact,  such as cholera, chicken pox, common cold and tuberculosis. Carriers: Insects and animals that carry disease-causing microbes and transfer them from one place to other are called carriers or vectors, such as house flies and mosquitoes.

How do houseflies transfer pathogens?

A housefly may sit on the garbage and animal excreta and the pathogens stick to their body. When they sit on uncovered food, these pathogens get transferred to the food. When someone eats this contaminated food, he or she may fall sick.

To avoid this, we must keep the food covered.

Name the carriers of:

Malaria

Female Anopheles mosquito (carries the parasite of malaria called Plasmodium)

Dengue

Female Aedes mosquito (carries the dengue virus called Flavivirus)

Common Diseases and their Modes of Transmission

How to prevent diseases that spread through air or contact?

To prevent diseases that spread through the air, keep the patient in complete isolation and keep his or her personal belongings away from others. Vaccination at the suitable age can prevent the onset of tuberculosis, chicken pox, polio, and measles.

How to prevent diseases that spread through water or food?

To prevent the spread of polio, cholera, typhoid and hepatitis A, vaccination is effective. One should also maintain personal hygiene and good sanitary habits and drink boiled drinking water.

One should also eat properly cooked food to avoid diseases like cholera.

How to prevent diseases that spread through mosquitoes?

We can stop the spreading of diseases caused by mosquitoes (such as malaria and dengue) by not allowing the mosquitoes to breed. We should keep our surroundings clean and dry, and not let water collect anywhere – in coolers, tyres, and flower pots etc.

We should also spray insecticides and use mosquito repellents and mosquito nets to protect ourselves from mosquito bites.

Common Diseases and the Microorganisms that cause them

Diseases Caused by Microorganisms in Animals

Anthrax: A dangerous disease that affects human and cattle is caused by a bacterium called Bacillus Anthracis.

Foot and mouth disease in Cattle: It is caused by a virus called Foot-and-mouth-disease Virus (FMDV) or Picornavirus.

Diseases Caused by Microorganisms in Plants

Microorganisms can cause diseases in plants and reduce crop yield. Some of the plants in which they cause diseases are:

The plants can be protected by using chemicals that kill these microbes.

Common Diseases in Plants caused by Microbes

Citrus Canker is caused by Bacteria and spreads through Air.

Rust of Wheat is caused by Fungi and spreads through Air or Seeds.

Yellow Vein Mosaic of Okra (Bhindi) is caused by Virus and spreads through Insects.

Food Preservation

Why do we need to preserve food?

We need to preserve food because microorganisms that grow on food can sometimes produce toxic substances which are poisonous to us. If we consume this spoilt food, we can become seriously ill or die. Hence, we need to preserve food from being spoilt.

Common Methods of preserving food are:

Nitrogen Fixation

Nitrogen constitutes 78% of our atmosphere.

In living organisms, it is found in:

• Proteins,
• Nucleic Acids,
• Chlorophyll, and
• Vitamins.

Atmospheric nitrogen cannot be used directly by the plants and animals. It gets fixed by either lightning or natural nitrogen fixers.

Nitrogen Cycle

A step-by-step explanation of Nitrogen Cycle

• Nitrogen Fixation: Atmospheric nitrogen is converted by lightning or certain bacteria like Rhizobium, Azotobacter and blue-green algae (present in soil) into compounds usable by plants.
• Nitrification: Ammonia conversion into nitrites by Nitrosomonas and further conversion of nitrites into nitrates by Nitrobacter. Plants take up nitrogen in form of ammonia or nitrates.
• Assimilation: Roots of plants absorb these nitrogenous compounds from soils and plants use them to synthesize proteins and other compounds.
• Animals feeding on plants get these proteins and nitrogen compounds.
• Ammonification: When plants and animals die, bacteria and fungi present in the soil convert the nitrogenous wastes into compounds that can be used by plants again.
• Denitrification:Nitrates can be converted  into nitrogen gas which is released back in the atmosphere by certain bacteria. Eg. Pseudomonas

Introduction

→ Human requires food for their survival as the energy obtained from the food is used for the various metabolic activities as Respiration, Excretion etc. We get our food from plants by Agricultural practices and animals too by the process of Animal husbandry (the branch of agriculture which deals with the rearing of animals-livestock). In order to provide food for a large population, regular production, proper management and distribution of food is necessary.
→ When plants of the same kind are grown and cultivated at one place on a large scale, it is called a crop. For example- wheat, rice, cereals, vegetables, fruits. These are classified on the basis of season in which they grow.
→ India is the India is a vast country. The climatic conditions like temperature, humidity and rainfall vary from one region to another. Accordingly, there is a rich variety of crops grown in different parts of the country.

Types of crops

→ Kharif Crops: The crops which are sown in the rainy season are called kharif crop. The rainy season in India is from June to September. For Example- Paddy, maize, soybean, groundnut, cotton  etc.
→ Rabi Crops: The crops grown in the winter season are Rabi crops. Their time Period is generally from October to March. For Example- Wheat, gram, pea, mustard and linseed.
(Paddy is not cultivated in summer season because it requires lot of water. Therefore, it is cultivated in rainy season)

Cultivation of crops include various Agricultural practice 

• Preparation of soil: The preparation of soil is the first step before growing a crop. One of the most important tasks in agricultural is to turn the soil and loosen it. This allows the roots to penetrate deep into the soil. The loose soil allows the roots to breathe easily even when they go deep into the soil. The loosened soil helps in the growth of earthworm and microbes present in the soil. These organisms are friends of the farmer since they further turn and loose the soil and add humus to it. only a few centimetres of the top layer of soil supports plant growth, turning and loosening of soil brings the nutrient-rich soil to the top so that plants can use these nutrients. Thus, turning and loosening of soil is very important for cultivation of crops.
→ The process of loosening and turning of the soil is called tilling or ploughing. This is done by using a plough. Ploughs are made of wood or iron. The ploughed field may have big pieces of soil called crumbs. Field is levelled for Sowing.

Agricultural Implements

(i) Plough: This is being used since ancient times for tilling the soil, adding fertilisers to the crop, removing the weeds, scraping of soil, etc. It contains a strong triangular iron strip called ploughshare. The main part of the plough is a long log of wood which is called a plough shaft.

The indigenous wooden plough is increasingly being replaced by iron ploughs nowadays.

• Hoe: It is a simple tool which is used for removing weeds and for loosening the soil. It has a long rod of wood or iron. A strong, broad and bent plate of iron is fixed to one of its ends and works like a blade. It is pulled by animals.

• Cultivator: Nowadays ploughing is done by tractor driven cultivator. The use of cultivator saves labour and time.

(ii) Sowing: Sowing is the most important part of crop production. Before sowing, good quality seeds are selected. Farmers prefer to use seeds which give a high yield.

• Traditional tool: The tool used traditionally for sowing seeds is shaped like a funnel. The seeds are filled into the funnel, passed down through two or three pipes having sharp ends. These ends pierce into the soil and place seeds there.

•  Seed drill: the seed drill is used for sowing with the help of tractors. This tool sows the seeds uniformly at proper distances and depths. It ensures that seeds get covered by the soil after sowing. This prevents damage caused by birds. Sowing by using a seed drill saves time and labour.
It is important to maintain the distance to avoid overcrowding of plants to ensure proper nutrients, sufficient sunlight and water.

(iii) Adding Manures and Fertilizers: The substances which are added to the soil in the form of nutrients for the healthy growth of plants are called manure and fertilisers. Continuous growing of crops makes the soil poorer in certain nutrients. Therefore, farmers have to add manure to the fields to replenish the soil with nutrients. This process is called Manuring. Improper or insufficient Manuring results in weak plants.

•  Farmers dump plant and animal waste in pits at open places and allow it to decompose. The decomposition is caused by some microorganisms. The decomposed matter is used as organic manure.

•  Fertilisers are chemical substances which are rich in a particular nutrient. Fertilisers are produced in factories. Some examples of fertilisers are urea, ammonium sulphate, super phosphate, potash, NPK(Nitrogen, Phosphorus, Potassium). But excessive use of fertilisers has made the soil less fertile. Fertilisers have also become a source of water pollution.

•  Another method of replenishing the soil with nutrients is through crop rotation.

Advantages of Manures
→ The organic manure is considered better than fertilisers.
→ It enhances the water holding capacity of the soil.
→ It makes the soil porous due to which exchange of gases becomes easy.
→ It increases the number of friendly microbes.
→ It improves the texture of the soil.

(iv) Irrigation: The supply of water to crops at different intervals is called irrigation. The time and frequency of irrigation varies from crop to crop, soil to soil and season to season
→ To maintain the moisture of the soil for healthy crop growth, fields have to be watered regularly. Water also protects the crop from both frost and hot air currents.
→ Sources of irrigation: The sources of irrigation are wells, tube wells, ponds, lakes, rivers, dams and canals.
• Traditional system: These methods are cheaper, but less efficient. The various traditional ways are:
→ Moat (pulley-system)
→ Chain pump
→ Dhekli, and
→ Rahat (Lever system)

• Modern method of Irrigation: Modern methods of irrigation help us to use water economically. The main methods used are as follows
→ Sprinkler System
→ Drip system

(v) Protection from weed
→ In a field many other undesirable plants may grow naturally along with the crop. These undesirable plants are called weeds.
→ The removal of weeds is called weeding. Weeding is necessary since weeds compete with the crop plants for water, nutrients, space and light. The best time for the removal of weeds is before they produce flowers and seeds. Weeds are also controlled by using certain chemicals, called weedicides, like 2,4-D. These are sprayed in the fields to kill the weeds. They do not damage the crops. The weedicides are diluted with water to the extent required and sprayed in the fields with a sprayer.

(vi) Harvesting
→ The cutting of crop after it is mature is called harvesting. In harvesting, crops are pulled out or cut close to the ground. It usually takes 3 to 4 months for a cereal crop to mature. Harvesting in our country is either done manually by sickle or by a machine called harvester.

→ In the harvested crop, the grain seeds need to be separated from the chaff. This process is called threshing. This is carried out with the help of a machine called ‘combine’ which is in fact a combined harvester and thresher. Farmers with small holdings of land do the separation of grain and chaff by winnowing.

(vii) Storage: Storage of produce is an important task. Before storing them, the grains are properly dried in the sun to reduce the moisture in them. This prevents the attack by insect pests, bacteria and fungi. Farmers store grains in jute bags or metallic bins. However, large scale storage of grains is done in silos and granaries to protect them from pests like rats and insects dried neem leaves are used for storing food grains at home. For storing large quantities of grains in big godowns, specific chemical treatments are required to protect them from pests and microorganisms.

Animal Husbandry

→ Animals reared at home or in farms, have to be provided with proper food, shelter and care. When this is done on a large scale, it is called animal husbandry.
→ Fish is good for health. We get cod liver oil from fish which is rich in vitamin D.

Numbers in General Form

The general form of a number is obtained by adding the product of the digits with there place values.

1. The General Form of a Two Digit Number

ab = a × 10 + b = 10a + b

Example

93 = 10 × 9 + 3

= 90 + 3

2. The General Form of a Three Digit Number

abc = 100 × a + 10 × b + c = 100a + 10b + c

Example

256 = 100 × 2 + 10 × 5 + 6

= 200 + 50 + 6

Remark: ab doesn’t mean a × b as we generally use it like this.

Games with Numbers

1. Reversing the Digits – Two Digit Number

a. The trick to divide by 11: If we have any two digit number then we will always get the remainder zero if we add the original number with its reverse number and divide it by 11. The trick behind it:

Step 1: Let us choose any two digit number ab, which can be written as (10a + b).

Step 2: Its reverse number will be ba, which can be written as (10b + a).

Step 3: Sum of both the numbers is ab + ba, we can also write as (10a + b) + (10b + a) = 11a+ 11b = 11 (a + b)

Step 4: By dividing the number by 11 we get 11 (a + b)/11 = (a + b) .

This shows that the remainder will always be zero in case of any number. The quotient is a + b, which is the sum of the digits of the given number ab.

Example

Try for the number 78.

Solution:

• The given number is 78.
• The reverse number is 87.
• Sum of both the numbers is 78 + 87 = 165, 165 ÷ 11 = 15 and the remainder are zero.

b. The trick to divide by 9: If we have any two digit number then we will always get the remainder zero if we subtract the original number with its reverse number and divide it by 9. The trick behind it:

Step 1: Let’s choose any two digit number ab, which can be written as (10a + b).

Step 2: Its reverse number will be ba, which can be written as (10b + a).

Step 3: By subtracting both the numbers i.e. ab – ba we get (10a + b) – (10b + a) = 9a – 9b = 9 (a – b)

Step 4: By dividing the number by 9 we get  9 (a – b)/9 = (a – b).

This shows that the remainder will always be zero in case of any number.

Example

Try for the number 78.

Solution:

• The given number is 78.
• The reverse number is 87.
• Subtraction of both the numbers is 87 – 78 = 9, 9 ÷ 9 = 1 and the remainder is zero.

2. Reversing the Digits – Three Digit Number

The trick to divide by 99: If we have any three digit number then we will always get the remainder zero if we subtract the original number with its reverse number and divide it by 99. The trick behind it:

Step 1: Let’s choose any three digit number abc, which can be written as (100a + 10b + c).

Step 2: Its reverse number will be cba, which can be written as (100c + 10b + a).

Step 3: By subtracting both the numbers i.e. abc – cba we get (100a + 10b + c) – (100c + 10b + a) = 99a – 99c = 99 (a – c).

Step 4: By dividing the number by 99 we get 99 (a – c)/9 = (a – c).

This shows that the remainder will always be zero in case of any number. 

Example

Try with the number 456

Solution:

• The given number is 456.
• The reverse number is 654.
• Subtraction of both numbers is 654-456=198
• By dividing it by 99 we get 2 i.e. 198 ÷ 99 = 2 and the remainder is zero.

3. Forming Three-digit Numbers with given three-digits.

If we have a three digit number then we will always get the remainder zero if we rearrange the number in such a way that all the three numbers are different and if we add them all and then divide it by 37. The trick behind it:

Step 1: Let us take any three digit number abc, which can be written as (100a +10b + c).

Step 2: Rearrange the number in such a way that it forms two different numbers. One number can be bca which can be written as (100b + 10c + a) and other can be cab which can be written as (100c + 10a + b).

Step 3: By adding all the three numbers i.e. abc +bca + cab we get (100a +10b + c) + (100b +10c + a) + (100c + 10a + b) = 111 (a + b + c)

Step 4: By dividing the number by 37 we will always get the remainder zero .

Example

Try for the number 397.

Solution:

• Given number is 397.
• By rearranging we will have two other numbers i.e. 973 and 739.
• Sum of all the three numbers is 397+ 973 + 739 = 2109.
• By dividing 2109 by 37 we get 57 i.e. 2109 ÷ 37 = 57 and remainder will be zero.

Letters for Digits

In this type of puzzles, the letter represents the digits and we have to crack the code. Generally, it has puzzles related to addition and multiplication.

Some important rules related to such types of puzzles:

• Every letter can represent only one digit and the vice-versa.
• The first digit cannot be zero Like 25 cannot be written as 025 and 0025.
• Every puzzle must have only one solution.

Example

Find the value of P & Q.

Solution:

Here, at the ones place the addition of P & Q is given 9. This shows that it is the sum of two single digits as the sum of two single digit numbers cannot be 19. Hence there is not any carry in this step. For the next step, 2 + P = 0 and as there was not any carry from the last step it is possible only if P = 8.
Now, 2 + 8 = 10 and 1 will be carry for the next step.
So, 1 + 1 + 6 = P. Hence, clearly, P is 8 and Q can only be 1 to satisfy the given addition.

Hence, the value of P is 8 and Q is 1.

1. Divisibility by 2: If the number ends with an even number i.e. 0, 2, 4, 6 and 8 then it will always be divisible by 2.

Example 

Check the number 23 and 630 are divisible by 2 or not.

Solution:

• 23 is not divisible by 2 as its one’s digit is an odd number.
• 630 is divisible by 2 as its one’s digit is 0 which is even number.

2. Divisibility by 3: If the sum of all the digits of the given number is divisible by 3, then that number will also be divisible by 3.

Example

Check the number 232 and 6300 are divisible by 3 or not.

Solution: 

• 232 is not divisible by 3 as its sum of the digits i.e. 2 + 3 + 2 = 7 is not divisible by 3.
• 630 is divisible by 3 as its sum of the digits i.e 6 + 3 + 0 = 9 is divisible by 3.

3. Divisibility by 4: If the last two digits of the number are divisible by 4 then that number will also be divisible by 4.​

Example

Check the number 1748 and 258 are divisible by 4 or not.

Solution:

• 1748 is divisible by 4 as the last two digits 48 is divisible by 4.
• 258 is not divisible by 4 as the last two digits 58 is not divisible by 4.

4. Divisibility by 5: If the number ends with ‘0’ or ‘5’ then it will always be divisible by 5.

Example

Check the number 23 and 630 are divisible by 5 or not.

Solution: 

• 23 is not divisible by 5 as its one’s digit is 3.
• 630 is divisible by 5 as its one’s digit is 0.

5. Divisibility by 6: To be divisible by 3 a number must be divisible by 2 and 3 both. i.e. you need to check for the divisibility test of 2 and 3 with that number. Or you can say that a number must end with even number and the sum of its digit should be divisible by 3 then that number will be divisible by 6.

Example

Check the number 2341 and 6300 are divisible by 5 or not.

Solution:

• 2341 is not divisible by 6 as its one’s digit is odd and its sum of digit 2+3+4+1 = 10 is not divisible by 3.
• 6300 is divisible by 6 as its one’s digit is even and the sum of its digits 6+3+0+0=9 is divisible by 3 i.e it is divisible by both 2 and 3 hence the number is divisible by 6.

6. Divisibility by 7: To check the number is divisible with 7 or not, we need to double the last digit of the number and then subtract the result from the rest of the digits and check whether the remainder is divisible by 7 or not.If the number of digits are very large then you need to repeat the process until you get the number which could be checked for the divisibility of 7.

Example

Check the number 203 is divisible by 7 or not.

Solution:

Given number is 203

• Double the last digit, 3 × 2 = 6
• Subtract 6 from the remaining number 20 i.e. 20 – 6 = 14
• The remainder 14 is divisible by 7 hence the number 203 is divisible by 7.

7. Divisibility by 8: If the last three digits form a number which is divisible by 8 then the whole number will be divisible by 8.

Example

Check the number 19640 is divisible by 8 or not.

Solution:

The last three digit of the number 19640 is 640.

640/8 = 80

As the number 640 is divisible by 8 hence the number 19640 is also divisible by 8.

8. Divisibility by 9: If the sum of all the digits of the given number is divisible by 9, then that number will also be divisible by 9.

Example

Check the number 232 and 6300 are divisible by 9 or not.

Solution:

• 232 is not divisible by 9 as its sum of the digits i.e. 2 + 3 + 2 = 7 is not divisible by 9.
• 630 is divisible by 9 as its sum of the digits i.e 6 + 3 + 0 = 9 is divisible by 9.

9. Divisibility by 10: If the number ends with zero then it will always be divisible by 10.

Example 1

Check the number 23 and 630 are divisible by 10 or not.

Solution:

• 23 is not divisible by 10 as its one’s digit is 3.
• 630 is divisible by 10 as its one’s digit is 0.

Example 2

If 31a5 is a multiple of 3, where a is a digit, what could be the values of a?

Solution:

As we know that the number will be divisible by 3 only if its digits sum is divisible by 3.

So let’s check the sum of its digits i.e. 3 + 1 + a + 5 = 9 + a which should be multiple of 3.

Here, a is a single digit number and also being added with 9, so any multiple of 3 can take place i.e. a can be 3 or 6 or 9 and as it is added by 9 so it could be zero also.

Hence, the value of a could be 0, 3, 6 or 9.

Graph

The graphs are the visual representation of the data collected in numerical form so that it could be easily understood. Graphs are generally used for comparisons between two or more data.

Types of Graph

1. Bar Graph

A bar graph is a type of graph which is used to show comparisons between different categories. In this type of graph, bars of uniform width are used to represent the different quantities and their height is proportional to their respective values.

This is the bar graph which shows the profit of the company over different years.

2. Double Bar Graph

This is the same as the bar graph but two types of data are shown here simultaneously. Generally, this type of graph is used to show a comparison between two data.

This Double bar graph shows the average temperature in different seasons in two different years. Green bars show the temperature in 1950 and pink bars show the temperature in 2000. Hence we can easily compare the up and downs in average temperature from 1950 to 2000.

3. A Pie Chart (Circle Graph)

When we represent the given data in the circular form then it is said to be a pie chart. It shows the part of a whole.

This pie chart shows the percentage of people watching different kind of movies. From this chart, we can easily get that the maximum number of people like romantic movies and the least number of people like drama movies.

4. Histogram

When we have grouped data in the form of class intervals then we can draw a histogram. It is also a bar graph but there is no gap between the bars as it is a graph of continuous data.

This histogram shows the distribution of people in a society according to their age.

5. Line Graph

When we need to see the changes continuously over a period of time then we use a line graph.

Here the horizontal line (x-axis) shows the number of days and vertical line (y-axis) shows the rainfall in mm on every successive day.

By this line graph, we can easily understand the changes in rainfall during these 9 days of a month.

Linear Graphs

A line graph which is a whole unbroken line is called a Linear Graph.

1. Location of a Point

For making a linear graph we use the Cartesian plane. It is that system on which we mark the points with the help of Vertical and Horizontal Lines.

This is a Cartesian plane which is like a square grid sheet. We make a horizontal line (x-axis) and a vertical line (y-axis) which divides it into four quadrants.

2. Coordinates of a Point

To write the coordinates of a point we need an x – coordinate and a y-coordinate of a point.

• x-coordinate tells how many units to move right or left. It is also called the Abscissa.
• y-coordinate tells how many units to move up or down. It is also called the Ordinate.
• While writing the coordinates of a point in the coordinate plane, the x – coordinate comes first, and then the y – coordinate. We place the coordinates in brackets.
• Coordinates of the point of intersection of x-axis and y-axis is (0, 0).this is called Origin.

In the above figure, OB = CA = x coordinate (Abscissa), and CO = AB = y coordinate (Ordinate).

We write the coordinate as (x, y).

Example

Plot the given points on the graph sheet.

• (2, 3)
• (-3, 1)
• (-1.5, – 2.5)

Solution:

Remark: If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.

Some Applications of Graph

In our day to day life, there are so many situations where we can use the graph for comparisons and analysis.

1. Independent Variable

Anything which is completely independent and its movement do not depend on any other factor then it is called Independent Variable.

2. Dependent Variable

Anything which increases or decreases with the movement of any other factor or it is dependent on any other factor then it is called Dependent Variable.

The Relationship between the Independent and Dependent Variable

The above graph shows that the revenue will increase with the increase in the number of cars washed. So the revenue is the dependent variable and the number of cars washed is an independent variable.

Factors of Natural Numbers

Factors are the pair of natural numbers which give the resultant number.

Example

24 = 12 × 2 = 6 × 4 = 8 × 3 = 2 × 2 × 2 × 3 = 24 × 1

Hence, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.

Prime Factor Form

If we write the factors of a number in such a way that all the factors are prime numbers then it is said to be a prime factor form.

Example

The prime factor form of 24 is

24 = 2 × 2 × 2 × 3

Factors of Algebraic Expressions

Like any natural number, an algebraic expression is also the product of its factors. In the case of algebraic expression, it is said to be an irreducible form instead of prime factor form.

Example

7pq = 7 × p × q =7p × q = 7q × p = 7 × pq

These are the factors of 7pq but the irreducible form of it is

7pq = 7 × p × q

Example

2x (5 + x)

Here the irreducible factors are

2x (5 + x) = 2 × x × (5 + x)

Factorisation

The factors of an algebraic expression could be anything like numbers, variables and expressions.

As we have seen above that the factors of algebraic expression can be seen easily but in some case like 2y + 4, x² + 5x etc. the factors are not visible, so we need to decompose the expression to find its factors.

Methods of Factorisation

1. Method of Common Factors

• In this method, we have to write the irreducible factors of all the terms
• Then find the common factors amongst all the irreducible factors.
• The required factor form is the product of the common term we had chosen and the leftover terms.

Example

2. Factorisation by Regrouping Terms

Sometimes it happens that there is no common term in the expressions then

• We have to make the groups of the terms.
• Then choose the common factor among these groups.
• Find the common binomial factor and it will give the required factors.

Example

Factorise 3x² + 2x + 12x + 8 by regrouping the terms.

Solution:

First, we have to make the groups then find the common factor from both the groups.

Now the common binomial factor i.e. (3x + 2) has to be taken out to get the two factors of the expression.

3. Factorisation Using Identities

Remember some identities to factorise the expression

• (a + b)²  = a² + 2ab + b²
• (a – b)²  = a² – 2ab + b²
• (a + b) (a – b)  = a² – b²

We can see the different identities from the same expression.

(2x + 3)² = (2x)²+ 2(2x) (3) + (3)²

= 4x² + 12x + 9

(2x – 3)² = (2x)² – 2(2x)(3) + (3)²

= 4x² -12x + 9

(2x + 3) (2x – 3) = (2x)² – (3)²

= 4x² – 9

Example 1

Factorise x– (2x – 1)² using identity.

Solution:

This is using the identity (a + b) (a – b) = a² – b²

x²– (2x – 1)² = [(x + (2x – 1))] [x – (2x-1))]

= (x + 2x – 1) (x – 2x + 1)

= (3x – 1) (- x + 1)

Example 2

Factorize 9x² – 24xy + 16y² using identity.

Solution:

1. First, write the first and last terms as squares.

9x² – 24xy + 16y² 

= (3x)² – 24xy + (4y)²

2. Now split the middle term.

= (3x)² – 2(3x) (4y) + (4y)²

3. Now check it with the identities

4. This is (3x – 4y)²

5. Hence the factors are (3x – 4y) (3x – 4y).

Example 3

Factorise x² + 10x + 25 using identity.

Solution:

x² + 10x + 25

= (x)² + 2(5) (x) + (5)²

We will use the identity (a + b) ² = a² + 2ab + b² here.
Therefore,

x² + 10x + 25 = (x + 5)²

4. Factors of  the form ( x + a) ( x + b)

 (x + a) (x + b) = x² + (a + b) x + ab.

Example:

Factorise x² + 3x + 2.

Solution:

If we compare it with the identity (x + a) (x + b) = x² + (a + b) x +ab

We get to know that (a + b) = 3 and ab = 2.

This is possible when a = 1 and b = 2.

Substitute these values into the identity,

x² + (1 + 2) x + 1 × 2

(x + 1) (x + 2)

Division of Algebraic Expressions

Division is the inverse operation of multiplication.

1. Process to divide a monomial by another monomial

• Write the irreducible factors of both the monomials
• Cancel out the common factors.
• The balance is the answer to the division.

Example

Solve 54y³ ÷ 9y

Solution:

Write the irreducible factors of the monomials

54y³ = 3 × 3 × 3 × 2 × y × y × y

9y = 3 × 3 × y

2. Process to divide a polynomial by a monomial

• Write the irreducible form of the polynomial and monomial both.
• Take out the common factor from the polynomial.
• Cancel out the common factor if possible.
• The balance will be the required answer.

Example

Solve 4x³ + 2x² + 2x ÷ 2x.

Solution:

Write the irreducible form of all the terms of polynomial

4x³ + 2x² + 2x

= 4(x) (x) (x) + 2(x) (x) + 2x

Take out the common factor i.e.2x

= 2x (2x² + x + 1)

3. Process to divide a polynomial by a polynomial

In the case of polynomials we need to reduce them and find their factors by using identities or by finding common terms or any other form of factorization. Then cancel out the common factors and the remainder will be the required answer.

Example

Solve z (5z² – 80) ÷ 5z (z + 4)

Solution:

Find the factors of the polynomial

 = z (5z² – 80)

= z [(5 × z²) – (5 × 16)]

= z × 5 × (z² – 16)

= 5z × (z + 4) (z – 4)  [using the identity a² – b² = (a + b) (a – b)]

Some Common Errors

• While adding the terms with same variable students left the term with no coefficient but the variable with no coefficient means 1.

2x + x + 3 = 3x + 3 not 2x +3

We will consider x as 1x while adding the like terms.

• If we multiply the expressions enclosed in the bracket then remember to multiply all the terms.

2(3y + 9) = 6y + 18 not 6y + 9

We have to multiply both the terms with the constant.

• If we are substituting any negative value for the variables then remember to use the brackets otherwise it will change the operation and the answer too.

If x = – 5

Then 2x = 2(-5) = -10

Not, 2 – 5 = – 3

• While squaring of the monomial we have to square both the number and the variable.

(4x)² = 16x² not 4x²

We have to square both the numerical coefficient and the variable.

• While squaring a binomial always use the correct formulas.

(2x + 3)² ≠  4x²+ 9 But (2x + 3)² = 4x² + 12x + 9

• While dividing a polynomial by a monomial remember to divide each term of the polynomial in the numerator by the monomial in the denominator.

Introduction to Direct and Inverse Proportions

There are so many situations in our life where we see some direct or indirect relationship between two things. Like

• If the number of things purchased is increasing then the amount to pay will also increase.
• If the speeds of the car will increase then the time to reach the destination will decreases.

Variations

If the value of two objects depends upon each other in such a way that the increase or decrease in the value of one object affects the value of another object then these two objects are said to be in variation.

Direct Proportion

Two quantities a and b are said to be in direct proportion if

• Increase in a increases the b
• Decrease in a decreases the b

But the ratio of their respective values must be the same.

• a and b will be in direct proportion if a/b = k(k is constant) or a = kb.
• In such a case if b₁, b₂ are the values of b corresponding to the values a₁, a₂ of a respectively then, a₁/b₂ = a₂/b₁​

This shows that as the no. of hours worked will increase the amount of salary will also increase with the constant ratio.

Symbol of Proportion

When two quantities a and b are in proportion then they are written as a ∝ b where ∝ represents “is proportion to”.

Methods to solve Direct Proportion Problems

There are two methods to solve the problems related to direct proportion-

1. Tabular Method

As we know that,

so, if one ratio is given then we can find the other values also. (The ratio remains the constant in the direct proportion).

Example

The cost of 4-litre milk is 200 Rs. Tabulate the cost of 2, 3, 5, 8 litres of milk of same quality.

Solution:

Let X litre of milk is of cost Y Rs.

X(Liter)	2	3	4	5	8
Y(Rupees)	Y2	Y3	200	Y4	Y5

We know that as the litre will increase the cost will also increase and if the litre will decrease then the cost will also decrease.

Given,

So the cost of 2 ltr milk is 100 Rs.

So the cost of 3 ltr milk is 150 Rs.

So the cost of 5 ltr milk is 250 Rs.

So the cost of 8 ltr milk is 400 Rs.

2. Unitary Method

If two quantities a and b are in direct proportion then the relation will be

k = a/b or a = kb

We can use this relation in solving the problem.

Example

If a worker gets 2000 Rs. to work for 4 hours then how much time will they work to get 60000 Rs.?

Solution:

Here, 

By using this relation a = kb we can find

Hence, they have to work for 12 hours to get 60000 Rs. 

Inverse Proportion

Two quantities a and b are said to be in Inverse proportion if

1. Increase in a decreases the b
2. Decrease in a increases the b

But the ratio of their respective values must be the same.

• a and b will be in inverse proportion if k= ab
• In such a case if b₁, b₂ are the values of b corresponding to the values a₁, a₂ of a respectively then, a₁b₁ = a₂b₂ = k, 
• When two quantities a and b are in inverse proportion then they are written as a ∝ 1/b

This shows that as the distance of the figure from light increases then the brightness to the figure decreases.

Example

If 15 artists can make a statue in 48 hours then how many artists will be required to do the same work in 30 hours?

Solution:

Let the number of artists required to make a statue in 30 hours be y.

Number of hours	48	30
Number of artists	15	y

We know that as the no. of artists will increase the time to complete the work will reduce. So, the number of hours and number of artists are in inverse proportion.

So 48 × 15 = 30 × y (a₁b₁ = a₂b₂)

Therefore,

So, 24 artists will be required to make the statue in 30 hours.