Every day we come across many changes that are taking place all around us. These changes may involve one or more substances. Sometimes, milk becomes sour. Souring of milk is a change. Making a sugar solution is a change. Similarly, setting of curd from milk is a change.
Some changes that we have noticed around us are melting of ice, making of ice cream, melting of wax, stretching a rubber band, evaporation of water, cutting of paper, breaking of glass pane, bending of glass tube by heating, boiling of water, sublimation of camphor, etc. Broadly, these changes are of two kinds:
Physical changes
Chemical changes
Physical Changes In a physical change, a substance undergoes changes only in its physical properties such as shape, size, colour and state, and no new substance is formed. First, we shall perform some activities to show the physical changes that are taking place all around us are:
Characteristics of Physical Changes The physical changes are temporary changes which can be easily reversed to form the original substance. In such a change, no new substance is formed. Thus, we noticed that the important characteristics of physical changes are as follows:
No new substance is formed in this change.
It is a temporary change and is generally reversible.
A temporary change in colour may take place.
Very little energy (heat, etc) is either absorbed or evolved.
Chemical Changes Chemical changes are also called chemical reactions. A chemical change occurs when two substances react chemically to form a new substance with different chemical properties. All the new substances which we use in various fields of our life are produced as a result of chemical changes (or chemical reactions).
A change with which we are quite familiar is the rusting of iron. Almost every iron (or steel) object kept in the open gets rusted slowly. It acquires a coating of a brownish substance called rust and the process is called rusting. We can usually see iron gates of parks or farmlands, iron benches kept in lawns and gardens, almost every article of iron, kept in the open gets rusted. The agricultural tools such as spades and shovels, also get rusted when exposed to the atmosphere for some time. In the kitchen, a wet iron pan (tawa) often gets rusted if left in that state for some time. Rust is not iron. It is different from iron on which it gets deposited.
When baking soda (NaHCO3) reacts with vinegar which contains acetic acid carbon dioxide comes out, which turns lime water milky, therefore it is a chemical change. In all these activities, we saw that in each change, one or more new substances are formed. When the magnesium ribbon was burnt, the ash was the new substance formed.
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In addition to new products, the following may accompany a chemical change:
Heat, light or any other radiation (e.g. ultraviolet) may be given off or absorbed.
The sound may be produced.
A change in smell may take place or a new smell may be given off.
A colour change may take place.
A gas may be formed.
Chemical Changes in Our Daily Life Chemical changes are very important in our lives. Indeed, every new material is discovered by studying chemical changes, e.g. If metal is to be extracted from an ore such as iron from iron ore, we need to carry out a series of chemical changes. Medicine is the end product of a chain of chemical reactions. Important and useful new materials such as plastics and detergents are produced by chemical reactions.
Let us consider some more examples of chemical changes. We saw from the activity that burning of magnesium ribbon is a chemical change. Burning of coal, wood or leaves is also a chemical change. In fact, burning of any substance is a chemical change. Burning is always accompanied in the production of heat and light.
An explosion of a firework (or crackers) is also a chemical change which produces heat, light, sound and unpleasant gases that pollute the atmosphere.
When food gets spoiled, it produces a foul smell. This shows that new substances have been formed in the spoiled food which has a foul smell. So, the spoilage of food is a chemical change.
If we cut an apple into slices and kept in the open for some time, we will find that the cut surface of apple acquires a brown colour. This change in colour is due to the formation of the new substance by the action of oxygen (or air). So, this change in colour is a chemical change.
Similarly, the cut surface of potato or brinjal turns black on keeping in air for some time due to the chemical change.
When an acid reacts with a base, then a neutralisation reaction takes place in which two new substances, salt and water, are formed. So, neutralisation is a chemical change.
During photosynthesis, the plants intake carbon dioxide and water in the presence of chlorophyll and sunlight to form two new substances, glucose (food) and oxygen. So, photosynthesis is a chemical change.
In the process of digestion, the various food materials break down to form new substances which can be absorbed by the body, so the process of digestion is a chemical change.
Rusting of Iron When an iron object is left exposed to moist air, it chemically reacts with oxygen and water in the air to form a red-brown flaky substance called rust. The process of rusting can be represented by the following equation: Iron (Fe) + Oxygen (O2) (From air) + Water (H2O) → Rust (Iron oxide, Fe2O3)
Rusting occurs in the presence of both oxygen and water. The more humid the air, the faster the rusting occurs. The rust slowly eats away or corrodes the iron, leading to considerable loss. Since iron is used in making bridges, ships, * cars, truck bodies and many other articles, the monetary loss due to the rusting is huge.
Preventions of Rusting Rusting can be prevented by not allowing the iron to come in contact with moisture and air. The simplest method is to coat the iron with oil, grease or paint. These coats should be applied regularly to prevent rusting.
A more efficient method is to coat the iron with another metal such as zinc or chromium. The process of depositing a layer of zinc on iron is called galvanisation. The iron pipes we use in our homes to carry water are galvanised to prevent rusting.
Rusting of ships is a major problem in the shipping industry as the body of a ship is always in contact with water and the air around it is also very humid. The salt in water speeds up the process of rusting. This leads to huge monetary loss to the shipping industry. Rusting of iron can be prevented by allowing it to make stainless steel. Stainless steel is made by mixing iron with carbon and metals like chromium, nickel and manganese. It does not rust.
Crystallisation Seawater contains salts dissolved in it which makes it salty. We have learnt in Class VI that salt can be obtained from seawater by the process of evaporation. The salt obtained in this manner is not pure and its crystals are small. The shape of the crystals cannot be seen clearly. Large crystals of pure substances can, however, be obtained from their solutions by the process of crystallisation. It is an example of a physical change. The process of cooling a hot concentrated solution of a substance to obtain crystals is called crystallisation. The process of crystallisation is used to obtain crystals of a pure solid substance from the impure solid substance.
An acid is a chemical substance that has a sour taste.
Many food items such as lemons, curd, vinegar and orange taste sour because of the presence of acid in them.
Acidic Substances are the substances that contain acid in them.
Natural Acids are the acids that occur in nature, for example, acids found in fruits are natural acids.
Bases
A base is a chemical substance that has a bitter taste and a soapy texture.
Bases are found in different substances such as bleach, ammonia, washing powder and soap.
Bases are also called Alkaline.
Basic Substances are the substances that contain a base in them.
Figure 1: Acids and Bases found in Nature
Neutral Substance is any substance which is neither acidic nor basic in nature.
Indicators
We cannot taste every object and find its nature. Therefore, we use indicators.
An indicator is a substance that can determine if another substance is acidic or basic in nature.
The indicators indicate the presence of an acid or base in a substance by changing their colour. For Example Turmeric, China rose petals and Litmus are some natural indicators. Natural indicators the indicators that occur in nature.
Litmus
Litmus is a natural indicator which is obtained from Lichens.
Litmus is available in a solution form and paper strips (red litmus and blue litmus paper).
Figure 2: Litmus test
Figure 3: Testing Solutions with Litmus Paper
Turmeric as an indicator
To use turmeric as an indicator it is generally mixed with water to form a paste which is then put on blotting paper and dried to form thin strips of turmeric paper.
The turmeric paper is then put into the solutions in order to determine their acidity or alkaline nature.
Sometimes turmeric solution is also used as an indicator.
Figure 4: Testing Substances with Turmeric Solution
China Rose
China Rose petals are kept in warm water and a coloured solution is obtained from that. This coloured solution is used as an indicator to test other substances.
Figure 5: Using China rose as an Indicator
Figure 6: Testing solutions with China rose
S.No.
Name of Acid/Base
Effect on litus paper
Effect on tumeric paper
Effect on China rose solution
1.
Hydrochloric acid
Blue litmus paper turns red
No change
Turns dark pink
2.
Sulphuric acid
Blue litmus paper turns red
No change
Turns dark pink
3.
Nitric acid
Blue litmus paper turns red
No change
Turns dark pink
4.
Acetic acid
Blue litmus paper turns red
No change
Turns dark pink
5.
Sodium hydroxide
Red litmus paper turns blue
Turns red
Turns green
6.
Ammmonium hydroxide
Red litmus paper turns blue
Turns red
Turns red
7.
Calcium hydroxide
Red litmus paper turns blue
Turns red
Turns red
Acid Rain
When the rainwater has increased amounts of acids in it, it is called Acid Rain.
The acid rain is formed because of the presence of air pollutants such as Nitrogen dioxide, Carbon dioxide and Sulphur dioxide in the air.
These pollutants mix with the rainwater and form acids such as Nitric acid, Sulphuric acid and Carbonic acid respectively.
The acid rain in severely affect the vegetation, animal life and even buildings of the region where it falls.
Figure 7: Acid Rain formation
pH scale
The measure of acidity or basic nature of a substance can be determined by its pH value.
The pH value range from 1 to 14 with 1 being the most acidic substance and 14 being the most basic substance while 7 is a neutral substance.
The pH value is generally determined by using pH strips or solutions
Figure 8: pH scale showing different colors
Acids are never stored in metal containers. They are rather stored in glass containers. This is so because acids are generally reactive in nature. If we keep them in metal containers they may react with the metal and erode them. Glass, on the other hand, does not react with acids at all.
Neutralization
Neutralization is a process or a chemical reaction in which an acidic and basic substance is mixed with each other in order to neutralize their acidic and alkaline nature.
The product that is formed after the neutralization process is called a Salt.
The salt can have basic, acidic or neutral nature.
The neutralization process results in the generation of heat which raises the temperature of the reacting mixture.
A synthetic indicator often used for testing neutralization reactions is Phenolphthalein solution. It is pink in color.
When an acid is added to Phenolphthalein solution, the solution turns colorless, indicating the presence of an acid.
When a base is added to Phenolphthalein solution, the solution retains its pink color, indicating the presence of a base.
Figure 9: Neutalization using Phenolphthalein
Formation of Salt
Figure 10: Formation of Salt
Neutralization in Everyday Life
1. Indigestion
We know that our stomach produces hydrochloric acid which helps in the digestion of food.
But sometimes the stomach releases too much of acid which leads to indigestion or sometimes hyperacidity.
Hence, we need to neutralize this acid by taking substances that are basic in nature commonly known as antacids.
For Example, milk of magnesia is a basic substance that can neutralize the acid of the stomach.
Figure 11: Indigestion caused in stomach
2. Ant Bite
The irritation of the skin due to ant bite is caused because of the presence of formic acid that the ant injects into the skin while biting.
Hence we use a basic substance to neutralize the effect.
For Example, baking soda or hydrogen carbonate, calamine solution or zinc carbonate are generally used to treat ant bites
3. Soil Treatment
Plants need a soil which is neutral in nature but using chemical fertilizers on soil can turn it into acidic.
To treat acidic soil we use quicklime (calcium oxide) or slaked lime (calcium hydroxide).
Basic soil can be treated by adding organic substances to it as they release acids while decomposing into the soil.
Figure 12: Soil treatment
4. Factory Wastes
The factory waste is acidic in nature and cannot be directly dumped anywhere. Hence bases are added to it before it falls off into a river or stream so that the aquatic life does not get affected.
Woollen clothes are obtained from animal fibres. Woollen clothes are generally dark in colour and are worn in the winter season as they protect us from the cold environment.
Cotton clothes are obtained from the plant fibres. The cotton clothes are generally light in colour and are worn in summer season so that we can feel cool.
Hot and Cold
We can understand if an object is hot or cold by the sense of touch. However, it can trick us sometimes. Therefore, we use a thermometer.
The temperature of an object: It is the degree of hotness or coldness of an object.
Thermometer: It is a device that can be used to find out how hot an object is. In other words, we use a thermometer to measure the temperature of an object.
Measuring the temperature of an object using a thermometer
Clinical thermometer
Figure 1 Clinical thermometer
It is a device that is used to measure the body temperature of a person.
It is made up of a glass tube of uniform thickness.
The glass tube contains a bulb at one end which is filled with Mercury.
The Mercury level in the thermometer rises up in the thread-like portion of the thermometer which therefore indicates the temperature of the body.
The level of the Mercury can be measured by reading the scale given on the thermometer.
The scale of the thermometer records the temperature in degree Celsius, generally, 35o C to 45o C, which is the range of human body temperature.
On an average, the temperature of the human body is around 37o C.
The clinical thermometer has a small sharp curve (kink) present near the bulb. This prevents the Mercury level from falling down on its own in the thermometer.
How to use the clinical thermometer?
Firstly, wash the thermometer with an antiseptic solution.
Before taking the temperature the thermometer is given a few jerks to bring down the level of Mercury below 35o C.
Then the thermometer is placed beneath the tongue for about a minute.
Then you can take it out and observe the temperature reading on the thermometer.
What precautions should be taken while using a clinical thermometer?
Wash the thermometer before and after using it.
Make sure the temperature of the thermometer is below 35o C before taking the temperature.
Keep the thermometer straight in order to see the Mercury level precisely.
It should always be held with care or it can break down. You should not touch the bulb of the thermometer at all.
Laboratory thermometer
Figure 2 Laboratory thermometer
The laboratory thermometer is used to find out the temperature of the other objects such as water rather than human body temperature. It can measure the temperature from -10o C to 110o C.
What precautions should be taken when using a laboratory thermometer?
Figure 3 Using Laboratory thermometer
You should always follow the same precautions as that of the clinical thermometer.
You should always hold the laboratory thermometer in a straight upright position without titling it.
The bulb of the thermometer should never touch the surface of the container in which the substance is kept.
However, the bulb of the thermometer should be completely immersed in the substance so that it covers the bulb from all the sides.
Other types of thermometers
Minimum-maximumthermometer: It is a thermometer used to measure the minimum and maximum temperature of the day by weather forecasters.
Figure 4 Minimum-maximum thermometer
Digital thermometer: It is sometimes difficult to handle a Mercury filled thermometer especially when it breaks and the mercury falls out. However, nowadays digital thermometers are available to use. This type of thermometer does not contain Mercury. It directly displays the correct temperature on a display screen.
Figure 5 Digital thermometer
The transfer of heat
The flow of heat always takes place from and hot object to a cold object.
Conduction: The process of flow of heat from a hot object to a cold object is called Conduction. Some objects can conduct heat while others cannot.
Figure 6 Conduction
Conductors: The objects that can allow the heat to flow through them are called Conductors. For Example, metals such as copper and aluminum.
Figure 7 Conductors
Insulators: The objects that do not allow the flow of heat from them are called Insulators. For Example, Wood and Plastic.
Figure 8 Insulators
Convection: The transfer of heat in liquids and gases is called Convection. The molecules of the liquid or gases that are near the source of the heat get heated first. They become lighter due to the heat and move upwards. The colder particles being heavier take the place and this process continues until the whole liquid or the gas gets heated. That is why the area above the flame of a candle always feels hot but the area on the sides of the candle does not.
Figure 9 Convection
Radiation: It is a process of transfer of heat in the form of waves. For Example, the sun’s heat reaches the Earth’s surface through radiation. Every hot object radiates some heat into the environment. Hence, many times an object gets heated just by being near to a hot object.
Figure 10 Radiation
Sea Breeze and Land Breeze
Sea Breeze
Figure 11 Sea Breeze
The wind blowing from the sea towards the land is called Sea Breeze.
During the daytime, the land in the coastal area gets heated due to the sun’s radiation.
The sea also gets heated, however it takes more time to get heated up than the land.
Hence the air above the land gets heated faster than the air above the sea.
The hot air from the land rises above as it is lighter and the cool air from the sea being heavier takes its place. This results in the sea breeze.
Land Breeze
The wind blowing from the land towards the sea is called the land breeze.
During the night time, the land in the coastal areas gets cool down faster than the sea. The air above the sea is hotter than the air above the land.
Therefore the air above the sea rises and the air from the land being cool flows towards the sea. This results in the land breeze.
Figure 12 Land breeze
Why do we wear light coloured clothes in summer?
The light coloured clothes reflect the heat back into the environment and keep us cool during the summer time.
Why do we wear dark coloured clothes in winters?
The dark colour clothes absorb the heat from the environment and keep us warm.
How do woollen clothes keep us warm?
The woollen clothes are a bad conductor of heat.
Therefore they do not allow the heat from the body to move out in the environment.
As a result, the air present between the woollen clothes and our body becomes hot and this makes us feel warm.
Similarly, two thin blankets provide more heat than one thick blanket because air can be trapped between the two thin blankets.
The wool is obtained mainly from animals like sheep, yak and goat. Wool is acquired from the fleece or hair of these animals.
Figure 1: Animals that yield wool
Production of Wool from Sheep
There are two types of fibres in sheep’s hair:
The Rough beard hair
The soft under hair which is present just near to the skin of the sheep
Wool is made from the soft hair the sheep because of its fine quality.
Selective Breeding: Sometimes sheep are selected to gain a breed that has only fine soft hair on the skin and less or no hard hair. This process is called Selective Breeding.
The sheep are generally fed with grass common leaves, call, pulses, oil cakes and dry fodder.
Sheep are reared (breed and raised) all over India in order to acquire wool from them such as in Jammu and Kashmir, Rajasthan, Arunachal Pradesh and Gujarat.
Figure 2: Different Types of Sheep found in India
The Process of obtaining Wool from the Hair Fibre of the Animals
Step 1: Shearing
It is a process of removing the fleece of the sheep along with a thin layer of its skin. Shearing is conducted generally in hot weather so that the sheep do not feel cold and can survive easily. The shearing process does not hurt the sheep because the upper part of the skin is normally dead skin.
Step 2: Scouring
It is a process of removing dirt, grease and dust from the hair removed from the sheep. It is generally done with the help of machines.
Step 3: Sorting
It is the process of separating the hair of the sheep according to their textures.
Step 4: Removing of burrs
In this step, the burrs or small fibres present on the hair are picked out. Then the hair is cleaned and dried out. The product so obtained is the wool that can now be converted into fibres.
Step 5: Coloring of wool fibres
In this step, the fibres are dyed in different colours.
Step 6: Rolling of wool
In the last step, the fibres for wool so obtained is straightened out combed and then rolled into a yarn.
Figure 3: The Process of Obtaining Wool
Occupational Hazard
In some industries, the workers have to face risks of getting diseases and sometimes death. These are called occupational hazards. Sorter’s disease is an occupational hazard associated with the production of wool. The people who sort the wool can get infected by bacteria called Anthrax. This bacterium infects the blood of the person which can lead to fatal death.
The Production of Silk
Silk is obtained from silkworms.
Sericulture: is the breeding and raising of silkworms in order to obtain silk from them.
Figure 4: Different Types of Silkworms and silk obtained from them
The Silk Moth
Figure 5: Life Cycle of Silk Moth
When the eggs of the silk moth hatch larvae are produced called Caterpillar or Silkworms.
The next stage of the caterpillar’s life is called the Pupa.
To enter into this stage the Caterpillar weaves a net that can hold it.
The Caterpillar then swings its head in the shape of an eight.
As it swings its head ,fibre is secreted.
This fibre is made up of protein and as it comes in contact with air it hardens and forms the Silk fibre.
The Caterpillar then covers itself into silk and turns into Pupa.
The covering of the Caterpillar is called the Cocoon.
Then the Caterpillar turns into a silk moth inside this covering.
The Silk thread on the Silk yarn is obtained from the cocoon.
Different types of silk are obtained because of the different types of silk moths.
The Mulberry Silk Moth is the most common kind of silk moth that produces soft elastic and shining silk.
The Process of obtaining Silk from the Silkworms
Figure 6: Rearing of Silkworms
Rearing: the silkworm farmers buy the eggs of the Silkmoth and raise them.
These eggs are generally large in numbers as a single silk moth can lay about 100 eggs at a time.
These eggs are stored in an environment having an appropriate temperature, humidity and hygienic conditions.
In order to hatch the larvae out of the eggs are heated.
They are then kept in a bamboo tray.
This process is conducted generally when the fresh leaves appear on the Mulberry trees so that the Caterpillar can get enough feed.
The Caterpillar feeds for around 25 to 30 days and then moves into a chamber in the tray to build a cocoon.
The cocoon when spun gets attached to the rocks present in the Bangalore train.
Processing of Silk
Firstly, as the cocoons are acquired they are kept under the sun or boiled so that the Silk fibres can separate out from them.
Then, the reeling of the silk takes place. It is a process in which the cocoon’s threads are processed to be used as silk.
The silk fibres thus obtained are drawn and rolled into threads.
All animals require food for obtaining energy, growth, repair of damaged parts and functioning of the body. The process of taking food by an animal and its utilisation in the body is called animal nutrition.
Plants can prepare their own food by the process of photosynthesis but animals get their food from plants, either directly by eating plants or indirectly by eating other animals that eat plants. Some animals eat both plants and other animals.
Animal nutrition includes nutrient requirements mode of intake of food and its utilisation in the body.
The components of food such as carbohydrates are complex substances which cannot be utilised by the body. So, they are broken down into simpler substances. The process of breakdown of complex components of food into simpler substances is called digestion. There are two methods of digesting food, i.e. physical method (including chewing and grinding of food in mouth) and chemical method (addition of digestive juices to the food by the body itself).
Different Ways of Taking Food Different types of animals show different modes of nutrition. Some animals filter tiny food particles and feed upon them, while some swollen the animals they prey upon. The mode of nutrition in different animals depends upon the special structure or organ for taking food inside the body.
Various modes of feeding in different Animals
Name of the animal
Kinds of food
Modes of feeding
Snail
Algae
Scraping from rocks
Ant
Plant material and other animals
Biting and chewing
Eagle
Flesh of prey
Tearing
Humming Bird
Nectar from flower
Sucking
Lice
Blood from the skin of scalp
Sucking
Mosquito
Blood from animals
Sucking
Butterfly
Nectar from flower
Syphoning
Housefly
Filth and refuses
Sucking
Amoeba
Tiny aquatic animals
Capturing and Swallowing
Snake (Python)
Animal as a whole
Swallowing
Starfish It is a marine animal which is covered by hard shells of calcium carbonate. It has a unique mode of nutrition. It opens the shell of its prey and pops out its stomach through its mouth surrounding the soft body of its prey. The starfish after capturing its prey brings bach its stomach inside its own body. This food is then digested slowly by starfish.
Digestion in Humans The food components pass through a continuous canal and get digested in each compartment. This is called an alimentary canal, it is ‘the tract or canal running from mouth to anus of human being where digestion and absorption of food take place.’ The alimentary canal can be divided into various compartments:
The buccal cavity
Food pipe or oesophagus
Stomach
Small intestine
Large intestine ending in the rectum
The anus
The main digestive glands which secrete digestive juices are
salivary gland
liver
pancreas
Various processes involved in utilisation of food in humans are
The process of taking food into the body is called ingestion.
The process by which the food containing large insoluble substances is broken down into small water-soluble substances is called digestion. There are two methods of digesting food, i.e. physical method (including chewing and grinding of food in mouth) and chemical method (addition of digestive juices to the food by the body itself).
The process by which the digested food passes through the intestinal wall into the bloodstream is called absorption.
The process by which the absorbed food is taken in body cells and used for energy, growth and repair is called assimilation.
The process by which the undigested food is removed from the body is called egestion.
Carbohydrates, fats and proteins are large insoluble substances which cannot pass through the walls of our intestine and get absorbed in that form. Therefore, these substances are broken down into small water-soluble substances. This is done by the process of digestion.
The carbohydrates get broken down into simple sugar called glucose, while fats in fatty acid and glycerol and proteins get broken down into amino acids during digestion. These simpler compounds are easily absorbed by the walls of small intestine into the blood.
Human Digestive System The system that consists of the digestive tract along with glands is called the digestive system. Now, let us know what happens to the food in different parts of the digestive tract.
1. Mouth and Buccal Cavity The process of ingestion starts from the mouth or buccal cavity. As we ingest, food the salivary glands present in the mouth start its digestion. The teeth present in the buccal cavity cut the food into small pieces by chewing and grinding it. Salivary glands secrete a watery liquid, saliva. This saliva contains digestive enzymes which help in partial digestion of food (starch). The tongue helps in mixing saliva with food. This partially digested food is swallowed by the tongue and passed down to oesophagus or food pipe.
Teeth The food is cut by the teeth inside the mouth. Teeth mechanically break the food into small pieces. These teeth vary in appearance. Each tooth is rooted in a separate socket in the gums. There are four types of teeth:
Incisors These are four chisel-shaped incisors at centre of each jaw for biting and cutting the food.
Canines These are two large pointed teeth just behind incisors in each jaw, for piercing and tearing the food.
Premolars These are four (two on each side) large premolars with the flat surface behind the canines in each jaw, for grinding and chewing.
Molars In an adult, these are six (three on each side) large molars with the flat surface behind the premolars in each jaw, for grinding.
Milk Teeth and Permanent Teeth In human beings, teeth grow twice. The sets of teeth that grow during infancy (when one is a small baby), are called milh teeth. These are also called as temporary teeth. These teeth get loosen and fall off at the age of 6-8 years. When milh teeth fall off, a new sets of teeth grow in their place. This second set of teeth is called permanent teeth because these remain till the old age. But if these teeth fall down, no new teeth arise on its place.
Sweets and Tooth Decay The tooth is covered by white, hard outer covering of tooth called enamel below which dentine is present. It is similar to bone which protects the pulp cavity having nerves and blood vessels. Bacteria are present in our mouth but they are not harmful to us. However, if we do not clean our teeth and mouth after eating, many harmful bacteria also begin to live and grow in it. These bacteria breakdown the sugars present from the leftover food and release acids. The acids gradually damage the teeth. This is called tooth decay.
Therefore, tooth decay is defined as the process of rotting of tooth and formation of cavity or holes in it which leads to the toothache.
When the holes or cavity reaches to the pulp cavity, it causes pain. If these cavities are not treated on time it causes severe toothache and may result in tooth loss.
Tooth decay can be prevented by adopting the following measures.
One should rinse and clean its teeth thoroughly after every meal.
We should clean our teeth with the help of datun or brush and toothpaste, twice a day.
We should use dental floss which is a special strong thread. It is moved between two teeth to take out trapped food particles.
Dirty fingers or unwashed objects must be avoided to put in the
We should avoid the use of sweets, chocolates, toffees, ice-cream, be avoided.
Tongue It is a muscular organ attached at the back to the floor of the buccal cavity. It is free from the front and can help in mixing saliva with the food, swallowing the food, talking or speaking and tasting with the help of taste buds for sweet, salt, sour and bitter food. Salivary glands secrete saliva which breaks down starch into sugars.
2. The food pipe or Oesophagus It is the tube-like structure which connects the mouth to the stomach and runs along neck and chest. It carries slightly digested food from the mouth to the stomach. Food is pushed downward by a wave like movement of the wall of foodpipe as a result of alternate contraction and relaxation. This movement is called peristalsis.
The chewed food that enters the oesophagus from mouth and is passed down to stomach is called bolus. Sometimes, food is not accepted by our stomach and is vomited out because the food moves in the opposite direction, i.e. from stomach to mouth by anti-peristaltic movement in oesophagus. Our windpipe (that carries air from nostril to our lungs) and foodpipe runs adjacent to each other. Air and food share a common passage in the throat. When we swallow food, a flap-like valve closes the passage of the windpipe and guides the food into the foodpipe. But if we laugh or talk while eating, the windpipe remains open and food particle enters into the windpipe and we experience hiccups, cough or choking si characteristic ‘gulping sound’ repeatedly and coughing clears the blockage of windpipe
3. The Stomach The stomach was first discovered by an American doctor William Beaumont in 1822 accidentally in the man named Alexis St. Martin. It is a thick walled bag-like structure which is present on the left side of the abdomen. Its shape is like flattened U and it is the widest part of the alimentary canal. The semi-digested food from oesophagus enters into stomach where further digestion takes place.
The churning of food into stomach takes place for three hours. The food is broken down into smaller pieces and forms semi-solid paste. The inner lining of stomach secretes mucus, hydrochloric acid and digestive enzymes or juices. The function of mucus is to protect the lining of stomach from the action of hydrochloric acid. The secretion of hydrochloric acid makes the medium acidic inside the stomach. It kills the harmful bacteria present in the food and also helps in the digestion of proteins in the stomach. The partially digested food which moves from stomach to the small intestine is called chyme.
4. The Small Intestine It is highly coiled long tube with length of about 7.5 metres. The small intestine is a narrow tube which receives secretions from the liver and pancreas. The wall of small intestine also secretes digestive juices. The complete digestion of food takes place inside the small intestine and the food components are also absorbed here.
The largest gland of the body, i.e. liver is the reddish-brown coloured gland, situated in the upper part of the abdomen on the right side. It secretes bile juices which is stored in a sac-like structure called as gall bladder. The bile helps in the digestion of fats. It breaks the fat molecules into tiny droplets so that its further breakdown into simpler compounds, becomes easy. The complete digestion of fats is done by pancreatic juice.
The pancreas is a large cream coloured gland which is located just below the stomach and secretes pancreatic juices. It breaks down fats into simpler compounds like fatty acid and glycerol, carbohydrate into simple sugars and proteins into simpler amino acids. The intestinal juices secreted by the walls of small intestine also help in the digestion of carbohydrate and proteins into simpler and water soluble substance. Now, the food is said to be digested. This digested food is now absorbed by the walls of small intestine.
Absorption in the Small Intestine The blood vessels in the walls of the intestine absorb the digested and water soluble substance to produce energy for growth and development of animals. The inner walls of small intestine have thousands of finger-like outgrowths called villi. These villi help in increasing the surface area of small intestine for the absorption of digested food. Villi possess a network of thin and small blood vessels close to its surface. These blood vessels absorb the digested food material and transport it to the different organs of the body where these are used to build repair the body and to provides energy.
The glucose breaks down into carbon dioxide and water and releases huge amount of energy with the help of oxygen inside the cell. Fatty acid and glycerol help in building the component of cells and form fats which is stored in the body as food reserve while amino acid is used in growth and repair of the body. The undigested food material is not absorbed by the small intestine and it passes from here to the large intestine.
5. Large Intestine It is a 1.5-meter long tube. It is wider and shorter than the small intestine. The undigested semi-solid food is passed from small intestine to large intestine. The large intestine absorbs water and salt from the undigested food. The remaining waste material then passes to the rectum and remains there for some time in the form of semi-solid faeces. This waste faecal matter is then removed through the anus from the body by the process called egestion.
Diarrhoea It is a condition in which a person passes out watery stools frequently. It is a disease which is caused by an infection, food poisoning or indigestion. It usually occurs In children and may be fatal. In this condition, there is a loss of water and salts from the body of a person through frequent watery stools. This loss of water from the body of a person through watery stool is called dehydration and it may be fatal under severe conditions. Diarrhoea should never be neglected. In order to prevent dehydration, the person suffering from diarrhoea should be given a solution of sugar and salt in the clean water for several times in a day.
This solution is called Oral Rehydration Solution (ORS). The ORS makes up the loss of water and salt in the body and sugar provides energy which helps in the recovery of disease. The dehydration of body can be prevented during diarrhoea by giving ORS solution regularly to the patients. In the mean time, the doctors should be called for medicines to cure of diarrhoea.
Digestion in Grass-Eating Animals The herbivorous animals such as cow, buffaloes, etc eat grass. These animals quickly swallow the grass and store it in a part of stomach called rumen. The food is not chewed completely. Rumen possess cellulose digesting bacteria which breakdown the food by fermentation. This partially digested food or grass present in the rumen of cow is called cud.
This cud is brought back into the mouth of the cow from the rumen into small lumps and animal chews it again. This process is called rumination and animals are called ruminants.
When this cud is thoroughly chewed in the mouth of the cow, it is swallowed again. This time the chewed cud does not go back to rumen but enter into the other compartments of cow’s stomach and then into the small intestine for complete digestion and absorption of food. The cellulose digesting bacteria are not present in the body of human being, therefore human beings and other carnivore cannot digest cellulose present in plant food items.
Feeding and Digestion in Amoeba Amoeba is a microscopic single-celled organism, which is found in pond water. It is a very simple animal and cannot be seen by naked eyes. Amoeba has a cell membrane, a rounded dense nucleus and many small bubble-like vacuoles in its cytoplasm. These vacuoles are of two types, i.e. food vacuole and contractile vacuole. Food vacuole contains food surrounded by water while contractile vacuole contains liquid or water and controls water regulation activity in Amoeba. Its shape is not fixed, i.e. it constantly changes its shape and position. The body of Amoeba has finger-like projections, called pseudopodia or false feet. It captures food and helps in locomotion of Amoeba. The food of Amoeba are microscopic organisms like tiny plants and animals present in pond water. When Amoeba senses its food, it pushes out pseudopodia around the food particle and engulfs it. The two pseudopodia join around the food particle and trap the food particle with a little water forming vacuole around food, thus the food gets trapped. Digestive juices present inside the vacuole, acts on the food and break it into simpler substances. This digested food is then absorbed and is used for growth, maintenance and multiplication of Amoeba. The undigested food residue is expelled outside by the vacuole. The basic process of digestion of food and release of energy is as similar to the other organisms.
All living organisms require food. The food gives energy to the organisms for growth and maintenance of their body functions. Carbohydrates, proteins, fats, vitamins and minerals are the components of food. These components of food are necessary for our body and are called nutrients.
Nutrition is the process of taking food by an organism and its utilisation by the body. Green plants prepare their own food while humans and animals are directly or indirectly dependent on plants for their food.
Modes of Nutrition On the basis of a different mode of nutrition, organisms are categorised into two major types, i.e.
(i) Autotrophs (auto-self, trobpos-nourishment) Autotrophic nutrition is the mode of nutrition in which organisms make their own food from the simple substance (e.g. CO2 and H2O) by the process of photosynthesis. Therefore, plants are called autotrophs.
(ii) Heterotrophs (heteros-other) Humans and animals do not contain chlorophyll and are dependent on plants for their food in readymade form. Those organisms which cannot prepare their own food and take food from green plants or animals are called heterotrophs and the mode of nutrition is called heterotrophic nutrition.
Photosynthesis: Food Making Process in Plants The process by which autotrophic green plants make their own food from simple inorganic substances (carbon dioxide and water) in the presence of sunlight and green pigment or chlorophyll is known as photosynthesis.
Site of Photosynthesis The process of photosynthesis takes place in green leaves, therefore leaves are referred to as the food factories of plants. The. the photosynthetic process can occur in other green parts of the plant-like stem but is not enough for meeting all the needs of the plant.
Reactions Involved in Photosynthesis The whole process of photosynthesis can be given by the following equation:
Cells All living organisms are made from small building units of catted cells. Cells are the structural and functional units of the body of all living organisms. They can only be seen under a microscope. The cell has a thin outer boundary called cell membrane, a distinct, centrally located spherical structure called nucleus and jelly-the substance surrounding the nucleus called cytoplasm.
The inorganic raw material, i.e. CO2 is taken from the air through the tiny pores present on the surface of leaves called stomata and water is absorbed through the roots of plants (from the soil) and is transported to leaves by vessels which act like pipes. These vessels form the continuous path from roots to leaves for the movement of nutrients.
Green plants possess chlorophyll in their leaves which captures the energy of the sunlight. This light energy is used to prepare food (starch). During the process, oxygen is also released. Photosynthesis is the unique process in which solar energy is captured by the leaves and stored in the plants in the form of food. Thus, ‘Sun is the ultimate source of energy for all the living organisms.’
Products of Photosynthesis The food produced by the process of photosynthesis is mainly carbohydrate. It produces glucose as food material which later gets converted into starch. The presence of starch in leaves indicates the occurrence of photosynthesis.
Importance of Photosynthesis If the plants do not perform photosynthesis, there would be no food on earth. Photosynthesis is also necessary for the production of oxygen gas in the atmosphere which is necessary for the respiration of organisms. Therefore, it can be said that no life is possible in the absence of photosynthesis.
Photosynthesis in Leaves of Various Colours In green pants, chlorophyll absorbs light energy from the sun to perform photosynthesis. Besides some green colour plants like Croton, maple, Colocasia, etc., have leaves that are red, brown, violet colour (variegated). These colours are present in large amounts and masks the green colour of chlorophyll in leaves. Thus, these leaves also perform photosynthesis and synthesise starch in them.
Synthesis of Plant Food other than Carbohydrates The starch or glucose is the simplest form of carbohydrate synthesised by the plants which is composed of carbon, hydrogen and oxygen. Sometimes these simplest forms of carbohydrate are utilised to synthesise other food nutrients like fats (oils), proteins, etc. Starch or glucose is rich in seeds like wheat, rice and various parts of plants like potato tuber. Sometimes the starch or glucose is stored in the form of oil in their seeds (oilseed), e.g. sunflower seed.
When the plant nutrient contains, carbon, hydrogen and oxygen along with nitrogen elements, it is called protein. The element nitrogen comes from soil in the form of nitrate by the actions of some bacteria present in soil and forms amino acid which is then converted into proteins. Therefore, plants also make fats and proteins as their food.
Other Modes of Nutrition in Plants There are some plants which do not contain chlorophyll in them and thus, cannot prepare their own food. These plants obtain their food from other plants or animal, i.e. they are heterotrophic in nature.
Parasitic Plants A parasitic plant is one that lines inside or outside the other organism and derive their food from them. The plant (non-green) which obtains their food from other organism is called a parasite and the living organism from whose body, food is obtained is called host, e.g. amarbel or Cuscuta. It takes readymade food from host through special type of roots called sucking roots which penetrate into host plant and suck food material from the host.
Insectivorous Plants There are some plants which can trap insects and digest them for their nutrition. These plants are green in colour but lack nitrogen elements. To overcome this problem, these plants eat insects. Hence they are called insectivorous plant or carnivorous plants. These have specialised leaves, the apex of which forms a lid that can open and close the mouth of pitcher. There are hair inside the pitcher which are used to entangle the insects.
When an insect comes in contact of the lid, it gets closed and traps the insects. The insect inside the pitcher is digested by digestive juices secreted by the pitcher to obtain nitrogen compounds (amino acids) from them. e.g. pitcher plant, sundew, Venus flytrap and bladderwort.
Since these can synthesise their own food but fulfil their nitrogen deficiency by eating insects, therefore these are called as partial heterotrophs.
Saprotrophic Plants The mode of nutrition in which organisms take their nutrients from dead and decaying matter is called saprotrophic nutrition. Plants which use the saprotrophic mode of nutrition are called saprotrophs, e.g. fungi like mushrooms are non-green plants that grow on the dead and decaying matter for their food. Bread moulds (fungi) and yeast are saprophytic plants.
Symbiotic Plants Sometimes, two plants of different species live together and help each other in obtaining food and shelter. This association is called symbiosis and such plants are called symbiotic plants. The relationship in which two different organisms live together and share shelter and nutrients is called symbiotic relationship, e.g. lichens and Rhizobium.
Lichen is an association in which algae and a fungus live together. The fungus provides shelter, water and minerals to the algae and in return, the algae provide food which it prepares by photosynthesis.
Replenishment of Nutrients in Soil Crops require a lot of nitrogen to make proteins. After the harvest, the soil becomes deficient in nitrogen. Plants cannot use the nitrogen gas available in the atmosphere directly. The action of certain bacteria can convert this nitrogen into a form readily used by plants. Rhizobium bacteria live in the root nodules of leguminous plants. These bacteria take nitrogen gas from the atmosphere and convert it into water-soluble nitrogen compounds making it available to the leguminous plants for their growth.
In return, leguminous plants provide food and shelter to the bacteria as Rhizobium cannot prepare its food. They, thus have a symbiotic relationship. This association is very important for the farmers, as they do not need to add nitrogen fertilisers to the soil in which leguminous plants are grown.
We hope the given CBSE Class 7 Science Notes Chapter 1 Nutrition in Plants Pdf free download will help you. If you have any query regarding NCERT Class 7 Science Notes Chapter 1 Nutrition in Plants, drop a comment below and we will get back to you at the earliest.
The figures which we can draw on a flat surface are called Plane Figures. They have two dimensions i.e. length and breadth, hence these are called 2 Dimensional Shapes.
Solid Figures (3-Dimensional Shape)
The figures which have three dimensions i.e. length, breadth and height are called 3 –Dimensional Shape. They occupy some space. Like the ball, box, tube etc.
Faces, Edges and Vertices
Faces – All the flat surfaces of the 3-D figure are the faces of that shape. The faces of 3D shapes are made by the 2-D shapes.
Edges – The line segment where the faces of the 3D shape meet with each other are the edges of that shape.
Vertices – The corners or the points where the edges meet with each other are the vertices of the 3D shape. The singular form of vertices is the vertex.
No. of Faces, Edges and Vertices in some common 3- D Shapes
S.No.
3 – D shape
Figure
Faces
Edges
Vertices
1.
Cube
6
12
8
2.
Cuboid
6
12
8
3.
Cone
2
1
1
4.
Sphere
1
1
0
5.
Cylinder
3
2
0
6.
Square based Pyramid
6
8
5
Nets for building 3 – D Shapes
If we draw the structure on the 2D form and fold it to make a 3D shape then it is said to be the net of that figure. Different figures have a different type of nets.
We can open a 3D shape from its edges to get the net of that figure.
Drawing Solids on a Flat Surface (2D representation of 3D Shapes)
As you know that the 3D shapes are the shapes which occupy some space but we can draw the 3D shapes on the flat surface also by some techniques. This is called a visual illusion.
1. Oblique Sketches
When we draw a shape in such a way that we are not able to see some of the faces of the 3D shape and the size of the length is also not equal but we are able to recognize that this is a cube then this is called an Oblique Sketch.
Steps to draw an Oblique Sketch
Draw the sketch of a cube with a side of 4 cm each.
Step 1: First, we need to draw a square of 2 × 2 on a grid sheet.
Step 2: Draw the opposite face of the same size which is offset to the front face.
Step 3: Now, join the respective corners, to form a cube.
Points to remember for the oblique sketch-
The front and back faces are of the same size.
All the edges are appearing as of the same length but their measurements are different.
2. Isometric Sketches
The isometric sheet is the sheet made up of dots which makes the equilateral triangles. When we draw the shape on the isometric sheet with the measurements proportional to the original figure then it is said to be Isometric sketch.
Visualizing Solid Objects
When we see any 3D shape from one side then some of its parts are not visible to us. But then also we can assume that which shape it is, this is called Visualization.
We can see that the front, top and side view of the above image is completely different and we cannot see some of its faces then also we can say that this figure is made up of four cubes.
Viewing different sections of a Solid
There are so many ways to see the different sections of the 3D shape-
1. View an object by Cutting or Slicing
When we cut any 3D object horizontally or vertically, we get a 2D face of that figure. This is called the Cross-section. The shape of the cross section depends upon the type of cut like horizontal or vertical.
If we give a horizontal cut to a rectangular pyramid then the cross section will be a rectangle in shape and if we cut it vertically then we get the shape of a triangle.
2. Viewing an object by its Shadow
If we throw the torchlight on any 3D object then we will get the shadow of that object on the plane in the form of 2D shape. The resultant shape depends upon the side of the object where we throw the light.
If we throw the light on the cylinder from its circular side then we will get the image of a circle.
If we throw the light on the cylinder while it is on standing position then its shadow will be rectangular in shape.
3. Viewing from different angles to get different views
All the 3D objects have a different view if we see them from different sides. By seeing them from different angles we can observe them easily.
In the above figure, we will have a different top view, front view and side view but we get the information about the shape of the figure by observing them.
If two or more parts of a figure are identical after folding or flipping then it is said to be symmetry. To be symmetrical the two halves of a shape must be of same shape and size.
If the shape is not symmetrical then it is said to be asymmetrical.
Line of Symmetry
It is an imaginary line which divides the image into two equal halves. It could be horizontal, vertical or diagonal. There could be one or more than one line of symmetry in a figure.
Lines of Symmetry for Regular Polygons
If all the sides and angles of a polygon are equal then it is said to be a regular polygon. Like the equilateral triangle, square etc.
All the regular polygons are symmetrical shapes.
In the regular polygon, the number of lines of symmetry is the same as the number of its sides.
Regular Polygon
Number of Sides
Line of Symmetry
Image
Equilateral Triangle
3
3
Square
4
4
Regular Pentagon
5
5
Regular Hexagon
6
6
Types of Symmetry
There are two types of Symmetry
1. Reflection Symmetry
If we draw a dotted line which gives the mirror reflection of the other half of the image then it is reflection symmetry. It is the same as basic symmetry which tells us that if the dotted line divides the image into two equal halves then it is the reflective symmetry of the figure.
2. Rotational Symmetry
If we rotate the image at a centre point of the image at 360° then the number of times the image looks the same, shows the rotational symmetry of the image.
Rotational Symmetry
If a figure rotates at a fixed point then that point is the centre of Rotation.
It could rotate clockwise or anticlockwise.
While rotation the measurement of the angle which we take is the angle of rotation. And a complete rotation is of 360°.
If the angle of rotation is 180° then it is called Half Turn and if the angle of rotation is 90° then it is called a Quarter Turn.
This image looks symmetrical but there is no line of symmetry in it i.e. there is any such line which divides it into two equal halves. But if we rotate it at 90° about its centre then it will look exactly the same. This shows that it has Rotational Symmetry.
While rotating, there are four positions when the image looks exactly the same. So this windmill has a rotational symmetry of order 4 about its centre.
Example
What is the Rotational symmetry of the given figure?
Solution:
To find the rotational symmetry, we have to find
The angle of rotation = 90°
Direction = clockwise
Order of rotation = 4
This shows that if the given figure rotates anticlockwise at 90° around its centre then it has rotational symmetry of order 4.
Line Symmetry and Rotational Symmetry
Some shapes have only line symmetry and some shapes have only rotational symmetry but there are some shapes which have both types of symmetry.
Example
Find whether the given image has rotational symmetry or line symmetry or both.
Solution:
Rotational Symmetry
If we rotate the image clockwise at an angle of 360° around its centre then it will have rotational symmetry of order 1 or no symmetry as every image will look same if we rotate it at 360°.
This will not look the same at every 120° because of the colour of the balls at its edges.
Line Symmetry
This figure will have three line of symmetry. As there are three possible lines which can divide the image into two equal halves.
Example
Tell whether the figures below have line symmetry or rotational symmetry or both.
Solution:
The first figure have 2 line of symmetry and rotational symmetry of order 2.
The second figure has no line of symmetry but have rotational symmetry of order 3.
The third figure has 1 line of symmetry but no rotational symmetry.
If we have to multiply the powers which have the same base then we have to add the exponents.
am × an = am + n
Example
83 × 84 = 83 + 4 = 87
2. How to divide powers with the same base?
If we have to divide the powers which have the same base then we have to subtract the exponents.
Example
3. How to take the power of a power?
If we have to take the power of a power then we have to multiply the exponents.
(am)n = amn
Example
(83)4 = 83 × 4 = 812
4. How to multiply the powers with the same exponents?
If we have to multiply the powers where the base is different but exponents are same then we will multiply the base.
ambm = (ab)m
Example
8343 = (8× 4)3 = 323
5. How to divide the powers with the same exponents?
If we have to divide the powers where the base is different but exponents are same then we will divide the base.
Example
6. Numbers with Exponent Zero
Any number with zero exponents is equal to one irrespective of the base.
a° = 1
Example
8° = 1
7. Numbers with Exponent One
Any number with one as the exponent is equal to the number itself.
a1 = a
Example
81 = 8
8. Power with a Negative Exponent
Negative exponents can be converted into positive exponents.
Example
Miscellaneous Examples
Example: 1
Example: 2
Expressing Large Numbers in the Standard Form
If we have to write very large numbers then to make them easy to read and understand we can write them in the standard form using decimals and exponents from 1.0 to 10.0.
An Algebraic Expression is the combination of constant and variables. We use the operations like addition, subtraction etc to form an algebraic expression.
Variable
A variable does not have a fixed value .it can be varied. It is represented by letters like a, y, p m etc.
Constant
A constant has a fixed value. Any number without a variable is a constant.
Example
1. 2x + 7
Here we got this expression by multiplying 2 and x and then add 7 to it.
In the above expression, the variable is x and the constant is 7.
2. y2
We get it by multiplying the variable y to itself.
Terms of an Expression
Terms
To form an expression we use constant and variables and separate them using the operations like addition, subtraction etc. these parts of expressions which we separate using operations are called Terms.
In the above expression, there are three terms, 4x, – y and 7.
Factors of a Term
Every term is the product of its factors. As in the above expression, the term 4x is the product of 4 and x. So 4 and x are the factors of that term.
We can understand it by using a tree diagram.
Coefficients
As you can see above that some of the factors are numerical and some are algebraic i.e. contains variable.The numerical factor of the term is called the numerical coefficient of the term.
In the above expression,
-1 is the coefficient of ab
2 is the coefficient of b2
-3 is the coefficient of a2.
Parts of an Expression
Here in the above figure, you can identify the terms, variables, constants and coefficients.
Like and Unlike Terms
Like Terms are the terms which have same algebraic factors. They must have the same variable with the same exponent.
Unlike Terms are the terms which have different algebraic factors.
2x2 + 3x – 5 does not contain any term with same variable.
2a2 + 3a2 + 7a – 7 contains two terms with same variable i.e. 2a2 and 3a2.so these are like terms.
Monomials, Binomials, Trinomials and Polynomials
Expressions
Meaning
Example
Monomial
Any expression which has only one term.
5x2, 7y, 3ab
Binomial
Any expression which has two, unlike terms.
5x2 + 2y, 2ab – 3b
Trinomial
Any expression which has three, unlike terms.
5x2 + 2y + 9xy, x + y – 3
Polynomial
Any expression which has one or more terms with the variable having non-negative integers as an exponent is a polynomial.
5x2 + 2y + 9xy + 4 and all the above expressions are also polynomial.
Remark: All the expressions like monomial, binomial and trinomial are also a polynomial.
Addition and Subtraction of Algebraic Expression
1. Addition of Like Terms
If we have to add like terms then we can simply add their numerical coefficients and the result will also be a like term.
Example
Add 2x and 5x.
Solution
2x + 5x
= (2 × x) + (5 × x)
= (2 + 5) × x (using distributive law)
=7 × x = 7x
2. Subtraction of Like Terms
If we have to subtract like terms then we can simply subtract their numerical coefficients and the result will also be a like term.
Example
Subtract 3p from 11p.
Solution
11p – 3p
= (11-3) p
= 8p
3. Addition of unlike terms
If we have to add the unlike terms then we just have to put an addition sign between the terms.
Example
Add 9y, 2x and 3
Solution
We will simply write it like this-
9y + 2x + 3
4. Subtraction of Unlike Terms
If we have to subtract the unlike terms then we just have to put minus sign between the terms.
Example
Subtract 9y from 21.
Solution
We will simply write it like this-
21 – 9y
5. Addition of General Algebraic Expression
To add the general algebraic expressions, we have to arrange them so that the like terms come together, then simplify the terms and the unlike terms will remain the same in the resultant expression.
While subtracting the algebraic expression from another algebraic expression, we have to arrange them according to the like terms then subtract them.
Subtraction is same as adding the inverse of the term.
Example
Subtract 4ab– 5b2 – 3a2 from 5a2 + 3b2 – ab
Solution
Finding the Value of an Expression
1. Expressions with One Variable
If we know the value of the variable in the expression then we can easily find the numerical value of the given expression.
Example
Find the value of the expression 2x + 7 if x = 3.
Solution
We have to put the value of x = 3.
2x + 7
= 2(3) + 7
= 6 + 7
= 13
2. Expressions with two or more variables
To find the value of the expression with 2 variables, we must know the value of both the variables.
Example
Find the value of y2 + 2yz + z2 if y = 2 and z = 3.
Solution
Substitute the value y = 2 and z = 3.
y2 + 2yz + z2
= 22 + 2(2) (3) + 32
= 4 + 12 + 9
= 25
Formula and Rules using Algebraic Expression
There are so many formulas which are made using the algebraic expression.
Perimeter Formulas
1. The perimeter of an equilateral triangle = 3l where l is the length of the side of the equilateral triangle by l and l is variable which can be varied according to the size of the equilateral triangle.
2. The perimeter of a square = 4l where l = the length of the side of the square.
3. The perimeter of a regular pentagon = 5l where l = the length of the side of the Pentagon and so on.
Area formulas
1. The area of the square = a2 where a is the side of the square
2. The area of the rectangle = l × b = lb where the length of a rectangle is l and its breadth is b
3. The area of the triangle = 1/2 × b × h where b is the base and h is the height of the triangle. Here if we know the value of the variables given in the formulas then we can easily calculate the value of the quantity.
Example
What is the perimeter of a square if the side of the square is 4 cm?
Solution
The perimeter of a square = 4l
l = 4 cm
4 × 4 = 16 cm
Rules for the Number Pattern
1. If we denote a natural number by n then its successor will always be (n + 1). If n = 3 then n + 1 will be 3 + 1 = 4.
2. If we denote a natural number by n then 2n will always be an even number and (2n + 1) will always be an odd number. If n = 3 then 2n = 2(3) = 6(even number), n = 3 then 2n + 1 = 2(3) + 1 = 7 (odd number)
3. If we arrange the multiples of 5 in ascending order then we can denote it by 5n. If we have to check that what will be the 11th term in this series then we can check it by 5n. n = 11 so 5n = 5(11) = 55.
Pattern in geometry
The number of diagonals which we can draw from one vertex of any polygon is (n – 3) where n is the number of sides of the polygon.
How many diagonals can be drawn from the one vertex of a hexagon?
The number of diagonals will be (n -3).
The number of sides in a hexagon is 8 so (n – 3) = (8 – 3) = 5
