Yearly Archives: 2022

Decimals

Introduction: Decimal

Decimal numbers are used to represent numbers that are smaller than the unit 1. Decimal number system is also known as base 10 system since each place value is denoted by a power of 10.

A decimal number refers to a number consisting of the following two parts:
(i) Integral part (before the decimal point)
(ii) Fractional Part (after the decimal point).
These both are separated by a decimal separator(.) called the decimal point.

A decimal number is written as follows: Example 564.8 or 23.97.
The numbers to the left of the decimal point increase with the order of 10, while the numbers to the right of the point increase with the decrease order of 10.
The above example 564.8 can be read as ‘five hundred and sixty four and eight tenths’
⇒5×100 + 6×10 + 4×1 + 8×(1/10)

A fraction can be written as a decimal and vice-versa. Example 3/2 = 1.5 or 1.5 = 15/10 = 3/2

Multiplication of Decimals

Multiplication of decimal numbers with whole numbers :
Multiply them as whole numbers. The product will contain the same number of digits after the decimal point as that of the decimal number.
E.g : 11.3×4 = 45.2

Multiplication of decimals with powers of 10 :
If a decimal is multiplied by a power of 10, then the decimal point shifts to the right by the number of zeros in its power.
E.g : 45.678×10 = 456.78 (decimal point shifts by 1 place to the right) or, 45.678×1000 = 45678 (decimal point shifts by 3 places to the right)

Multiplication of decimals with decimals :

Multiply the decimal numbers without decimal points and then give decimal point in the answer as many places same as the total number of places right to the decimal points in both numbers.

E.g :

Division of Decimals

Dividing a decimal number by a whole number:
Example: 45.2/55
Step 1. Convert the Decimal number into Fraction: 45.25= 4525/100
Step 2. Divide the fraction by the whole number: (4525/100)÷5 = (4525/100) × (1/5) = 9.05

Dividing a decimal number by a decimal number:
Example 1: 45.25/0.5
Step 1. Convert both the decimal numbers into fractions: 45.25 = 4525/100 and 0.5 = 5/10
Step 2. Divide the fractions: (4525/100)÷(5/10) = (4525/100)×(10/5) = 90.5
Example 2:

Dividing a decimal number by powers of 10  :
If a decimal is divided by a power of 10, then the decimal point shifts to the left by the number of zeros present in the power of 10.
Example: 98.765÷100=0.98765 Infinity

When the denominator in a fraction is very very small (almost tending to 0), then the value of the fraction tends towards infinity.
E.g: 999999/0.000001 = 999999000001 ≈ a very large number, which is considered to be ∞

1. How to multiply a decimal number with a whole number?

If we have to multiply the whole number with a decimal number then we will multiply them as normal numbers but the decimal place will remain the same as it was in the original decimal number.

Example

35 × 3.45 = 120.75

Here we have multiplied the number 35 with 345 as normal whole numbers and we put the decimal at the same place from the right as it was in 3.45.

2. How to multiply Decimal numbers by 10,100 and 1000?

a. If we have to multiply a decimal number by 10 then we will transfer the decimal point to the right by one place.

Example

5.37 × 10 = 53.7

b. If we have to multiply a decimal number by 100 then we will transfer the decimal point to the right by two places.

Example

5.37 × 100 = 537

c. If we have to multiply a decimal number by 1000 then we will transfer the decimal point to the right by three places.

Example

5.37 × 1000 = 5370

3. How to multiply a decimal number by another decimal number?

To multiply a decimal number with another decimal number we have to multiply them as the normal whole numbers then put the decimal at such place so that the number of decimal place in the product is equal to the sum of the decimal places in the given decimal numbers.

Example

Division of Decimal Numbers

1. How to divide a decimal number with a whole number?

If we have to divide the whole number with a decimal number then we will divide them as whole numbers but the decimal place will remain the same as it was in the original decimal number.

Example

12.96 ÷ 4 = 3.24

Here we divide the number 1296 with 4 as normal whole numbers and we put the decimal at the same place from the right as it was in 12.96.

2. How to divide Decimal numbers by 10,100 and 1000?

a. If we have to divide a decimal number by 10 then we will transfer the decimal point to the left by one place.

Example

5.37 ÷ 10 = 0.537

b. If we have to divide a decimal number by 100 then we will transfer the decimal point to the left by two places.

Example

253.37 × 100 = 2.5337

c. If we have to divide a decimal number by 1000 then we will transfer the decimal point to the left by three places.

Example

255.37 × 1000 = 0.25537

3. How to divide a decimal number by another decimal number?

To divide a decimal number with another decimal number

• First, we have to convert the denominator as the whole number by multiplying both the numerator and denominator by 10, 100 etc
• Now we can divide them as we had done before.

Example

Here we had converted denominator 2.4 in the whole number by multiplying by 10.Then divide it as usual

Introduction: Fractions

The word fraction derives from the Latin word “Fractus” meaning broken. It represents a part of a whole, consisting of a number of equal parts out of a whole.
E.g : slices of a pizza.

Representation of Fractions

A fraction is represented by 2 numbers on top of each other, separated by a line. The number on top is the numerator and the number below is the denominator. Example :34  which basically means 3 parts out of 4 equal divisions.

Fractions on the Number Line

In order to represent a fraction on a number line, we divide the line segment between two whole numbers into n equal parts, where n is the denominator.
Example: To represent 1/5 or 3/5, we divide the line between 0 and 1 in 5 equal parts. Then the numerator gives the number of divisions to mark.

Multiplication of Fractions

Multiplication of Fractions

Multiplication of a fraction by a whole number :
Example 1: 7×(1/3) = 7/3
Example 2 : 5×(7/45) = 35/45, Dividing numerator and denominator by 5, we get 7/9

Multiplication of a fraction by a fraction is basically product of numerators/product of denominators

Example 1: (3/5) × (12/13) = 36/65
Example 2 : Multiplication of mixed fractions

First convert mixed fractions to improper fractions and then multiply
143×87

Fraction as an Operator ‘Of’

The ‘of’ operator basically implies multiplication.

Example: 1/6 of 18 = (1/6)×18 = 18/6 = 3
or, 1/2 of 11 = (1/2) × 11 = 11/2 

Division of Fractions

Reciprocal of a Fraction

Reciprocal of any number n is written as1n
Reciprocal of a fraction is obtained by interchanging the numerator and denominator.
Example: Reciprocal of 2/5 is 5/2
Although zero divided by any number means zero itself, we cannot find reciprocals for them, as a number divided by 0 is undefined.
Example : Reciprocal of 0/7 ≠ 7/0

Division of Fractions

Division of a whole number by a fraction : we multiply the whole number with the reciprocal of the fraction.
Example: 63÷(7/5) = 63×(5/7) = 9×5 = 45

Division of a fraction by a whole number: we multiply the fraction with the reciprocal of the whole number.
Example: (8/11)÷4 = (8/11)×(1/4) = 2/11

Division of a fraction by another fraction : We multiply the dividend with the reciprocal of the divisor.
Example: (2/7) ÷ (5/21) = (2/7) × (21/5) = 6/5

Types of Fractions

Types of Fractions

Proper fractions represent a part of a whole. The numerator is smaller than the denominator.
Example: 1/4, 7/9, 50/51. Proper fractions are greater than 0 and less than 1

Improper fractions have a numerator that is greater than or equal to the denominator.
Example: 45/6, 6/5. Improper fractions are greater than 1 or equal to 1.

Mixed fractions are a combination of a whole number and a proper fraction.
Example: 43/5 can be written as .

Conversion of fractions : An improper fraction can be represented as mixed fraction and  a mixed fraction can represented as improper.
In the above case, if you multiply the denominator 5 with the whole number 8 add the numerator 3 to it, you get back 435

Like fractions : Fractions with the same denominator are called like fractions.
Example: 5/7, 3/7. Here we can compare them as (5/7) > (3/7)

Unlike fractions : Fractions with different denominators are called unlike fractions.
Example: 5/3, 9/2. To compare them, we find the L.C.M of the denominator.
Here the L.C.M is 6 So, (5/3)×(2/2) , (9/2)×(3/3)
⇒ 10/6, 27/6
⇒ 27/6 > 10/7

Introduction: Rational Numbers

• A rational number is defined as a number that can be expressed in the form, where p and q are integers and q≠0.
• In our daily lives, we use some quantities which are not whole numbers but can be expressed in the form of. Hence we need rational numbers.

Equivalent Rational Numbers

• By multiplying or dividing the numerator and denominator of a rational number by a same non zero integer, we obtain another rational number equivalent to the given rational number.These are called equivalent fractions.
• ∴andare equivalent fractions.
• 
  ∴andare equivalent fractions.

Rational Numbers in Standard Form

• A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.
• Example: Reduce.Here, the H.C.F. of 4 and 16 is 4.is the standard form of.

LCM

• The least common multiple (LCM) of two numbers is the smallest number (≠0) that is a multiple of both.
• Example: LCM of 3 and 4 can be calculated as shown below:
  Multiples of 3: 0, 3, 6, 9, 12,15
  Multiples of 4: 0, 4, 8, 12, 16
  LCM of 3 and 4 is 12.

Rational Numbers Between 2 Rational Numbers

Rational Numbers between Two Rational Numbers

• There are unlimited number(infinite number) of rational numbers between any two rational numbers.
• Example: List some of the rational numbers between −35 and −13.
  Solution: L.C.M. of 5 and 3 is 15.
  ⇒ The given equations can be written asand.
  ⇒ −615,−715,−815 are the rational numbers between −35 and −13.

Note: These are only few of the rational numbers between −35 and −13. There are infinte number of rational numbers between them. Following the same procedure, many more rational numbers can be inserted between them.

Properties of Rational Numbers

Properties of Rational Numbers

Addition of Rational Numbers

<

Subtraction of Rational Numbers

Multiplication and Division of Rational Numbers

Multiplication of Rational Numbers

Negatives and Reciprocals

Negatives and Reciprocals

Additive Inverse of a Rational Number

Representing on a Number Line

Rational Numbers on a Number Line

Comparison of Rational Numbers

Integers

A whole number, from zero to positive or negative infinity is called Integers. I.e. it is a set of numbers which include zero, positive natural numbers and negative natural numbers. It is denoted by letter Z.

Z = {…,-2,-1, 0, 1, 2…}

Integers on Number Line

On the number line, for positive integers we move to the right from zero and for negative integers move to the left of zero.

Facts about how to Add and Subtract Integers on the Number Line

1. If we add a positive integer, we go to the right.

2. If we add a negative integer, we go to the left.

3. If we subtract a positive integer, we go to the left.

4. If we subtract a negative integer, we go to the right.

The Additive Inverse of an Integer

The negative of any number is the additive inverse of that number.

The additive inverse of 5 is (- 5) and additive inverse of (- 5) is 5.

This shows that the number which we add to a number to get zero is the additive inverse of that number.

Number	Additive Inverse
5	– 5
14	– 14
– 10	10
– 6	6

Properties of Addition and Subtraction of Integers

1. Closure under Addition

For the closure property the sum of two integers must be an integer then it will be closed under addition.

Example

2 + 3 = 5

2+ (-3) = -1

(-2) + 3 = 1

(-2) + (-3) = -5

As you can see that the addition of two integers will always be an integer, hence integers are closed under addition.

If we have two integers p and q, p + q is an integer.

2. Closure under Subtraction

If the difference between two integers is also an integer then it is said to be closed under subtraction.

Example

7 – 2 = 5

7 – (- 2) = 9

– 7 – 2 = – 9

– 7 – (- 2) = – 5

As you can see that the subtraction of two integers will always be an integer, hence integers are closed under subtraction.

For any two integers p and q, p – q is an integer.

3. Commutative Property

a. If we change the order of the integers while adding then also the result is the same then it is said that addition is commutative for integers.

For any two integers p and q

p + q = q + p

Example

23 + (-30) = – 7

(-30) + 23 = – 7

There is no difference in answer after changing the order of the numbers.

b. If we change the order of the integers while subtracting then the result is not the same so subtraction is not commutative for integers.

For any two integers p and q

p – q ≠ q – p will not always equal. 

Example

 23 – (-30) = 53

(-30) – 23 = -53

The answer is different after changing the order of the numbers.

4. Associative Property

If we change the grouping of the integers while adding in case of more than two integers and the result is same then we will call it that addition is associative for integers.

For any three integers, p, q and r

p + (q + r) = (p + q) + r

Example

If there are three integers 3, 4 and 1 and we change the grouping of numbers, then

The result remains the same. Hence, addition is associative for integers.

5. Additive Identity

If we add zero to an integer, we get the same integer as the answer. So zero is an additive identity for integers.

For any integer p,

p + 0 = 0 + p =p

Example

2 + 0 = 2

(-7) + 0 = (-7)

Multiplication of Integers

Multiplication of two integers is the repeated addition.

Example

• 3 × (-2) = three times (-2) = (-2) + (-2) + (-2) = – 6
• 3 × 2 =  three times 2 = 2 + 2 + 2 = 6

Now let’s see how to do the multiplication of integers without the number line.

1. Multiplication of a Positive Integer and a Negative Integer

To multiply a positive integer with a negative integer, we can multiply them as a whole number and then put the negative sign before their product.

So the product of a negative and a positive integer will always be a negative integer.

For two integers p and q, 

p × (-q) = (-p) × q = – (p × q) = – pq

Example

4 × (-10) = (- 4) × 10 = – (4 × 10) = – 40

2. Multiplication of Two Negative Integers

To multiply two negative integers, we can multiply them as a whole number and then put the positive sign before their product.

Hence, if we multiply two negative integers then the result will always be a positive integer.

For two integers p and q,

(-p) × (-q) = (-p) × (-q) = p × q

Example

(-10) × (-3) = 30

3. The Product of Three or More Negative Integers

It depends upon the number of negative integers.

a. If we multiply two negative integers then their product will be positive integer

(-3) × (-7) = 21

b. If we multiply three negative integers then their product will be negative integer

(-3) × (-7) × (-10) = -210

If we multiply four negative integers then their product will be positive integer

(-3) × (-7) × (-10) × (-2) = 420

Hence, if the number of negative integers is even then the result will be a positive integer and if the number of negative integers is odd then the result will be a negative integer.

Properties of Multiplication of Integers

1. Closure under Multiplication

In case of multiplication, the product of two integers is always integer so integers are closed under multiplication.

For all the integers p and q

p×q = r, where r is an integer

Example

(-10) × (-3) = 30

(12) × (-4) = -48

2. Commutativity of Multiplication

If we change the order of the integers while multiplying then also the result will remain the same then it is said that multiplication is commutative for integers.

For any two integers p and q

p × q = q × p

Example

20 × (-30) = – 600

(-30) × 20 = – 600

There is no difference in answer after changing the order of the numbers.

3. Multiplication by Zero

If we multiply an integer with zero then the result will always be zero.

For any integer p,

p × 0 = 0 × p = 0

Example

9 × 0 = 0 × 9 = 0

0 × (-15) = 0

4. Multiplicative Identity

If we multiply an integer with 1 then the result will always the same as the integer.

For any integer q

q × 1 = 1 × q = q

Example

21 × 1 = 1 × 21 = 21

1 × (-15) = (-15)

5. Associative Property

If we change the grouping of the integers while multiplying in case of more than two integers and the result remains the same then it is said the associative property for multiplication of integers.

For any three integers, p, q and r

p × (q × r) = (p × q) × r

Example

If there are three integers 2, 3 and 4 and we change the grouping of numbers, then

The result remains the same. Hence, multiplication is associative for integers.

6. Distributive Property

a. Distributivity of Multiplication over Addition.

For any integers a, b and c

a × (b + c) = (a × b) + (a × c)

Example

Solve the following by distributive property.

I. 35 × (10 + 2) = 35 × 10 + 35 × 2

= 350 + 70

= 420

II. (– 4) × [(–2) + 7] = (– 4) × 5 = – 20 And

= [(– 4) × (–2)] + [(– 4) × 7]

= 8 + (–28)

= –20

So, (– 4) × [(–2) + 7] = [(– 4) × (–2)] + [(– 4) × 7]

b. Distributivity of multiplication over subtraction

For any integers a, b and c

a × (b – c) = (a × b) – (a × c)                      

Example

5 × (3 – 8) = 5 × (- 5) = – 25

5 × 3 – 5 × 8 = 15 – 40 = – 25

So, 4 × (3 – 8) = 4 × 3 – 4 × 8.

Division of integers

1. Division of a Negative Integer by a Positive Integer

The division is the inverse of multiplication. So, like multiplication, we can divide them as a whole number and then place a negative sign prior to the result. Hence the answer will be in the form of a negative integer.

For any integers p and q,

( – p) ÷ q = p ÷ (- q) = – (p ÷ q) where, q ≠ 0

Example

64 ÷ (- 8) = – 8

2. Division of Two Negative Integers

To divide two negative integers, we can divide them as a whole number and then put the positive sign before the result.

The division of two negative integers will always be a positive integer.

For two integers p and q,

(- p) ÷ (- q) = (-p) ÷ (- q) = p ÷ q where q ≠ 0

Example

(-10) ÷ (- 2) = 5

Properties of Division of Integers

For any integers p, q and r

Property	General form	Example	Conclusion
Closure Property	p ÷ q is not always an integer	10 ÷ 5 = 2 5 ÷ 10 = 1/2 (not an integer)	The division is not closed under division.
Commutative Property	p ÷ q ≠ q ÷ p	10 ÷ 5 = 2 5 ÷ 10 = 1/2	The division is not commutative for integer.
Division by Zero	p ÷ 0 = not defined 0 ÷ p = 0	0 ÷ 10 = 0	No
Division Identity	p ÷ 1 = p	10 ÷ 1 = 10	Yes
Associative Property	(p ÷ q) ÷ r ≠ p ÷ (q ÷ r)	[(–16) ÷ 4] ÷ (–2) ≠ (–16) ÷ [4 ÷ (–2)] (-8) ÷ (-2) ≠ (-16) ÷ (-2) 4 ≠ 8	Division is not Associative for integers.

POINTS TO REMEMBER

• The Isthmus of Panama joins South America to North America. South America is triangular in shape and a greater part of it lies south of the equator.
• South America can be divided into four physical divisions—the West Coastal Plains, the Andes Mountains, the Central Plains and the Eastern Highlands.
• The West Coastal Plains are narrow plains lying between the Pacific Ocean and the Andes Mountains, in the western part of the continent. The Atacama Desert is located here.
• The Andes are a long stretch of high, young fold mountains that run parallel to the Pacific Coast in the western part of the continent. Mt Aconcagua, the highest peak in South America, and Lake Titicaca, the second highest freshwater lake in the world, are located here. There are also several active dormant volcanoes located here such as Mt Chimborazo and Mt Cotopaxi.
• The Central Plains are lowlands that lie between the Andes in the west and the Eastern Highlands in the east. The flat plains are formed by the rivers Amazon, Orinoco, Parana, Paraguay and Uruguay.
• The Guiana Highlands and the Brazilian Highlands form the Eastern Highlands. The two highlands are separated by the river Amazon. These highlands extend in the eastern part of the continent along the Atlantic coast.
• The Orinoco River, the Magdalena River and the Amazon River are some of the important rivers of South America. Rivers Paraguay, Parana and Uruguay form the La Plata river system. Lake Titicaca, Lake Poopo and Lake Maracaibo are the important lakes of die continent.

IMPORTANT TERMS

Llanos : The grasslands of the Orinoco Basin.
Selvas : The dense equatorial forest of the Amazon Basin.
Pampas : The extensive temperate grasslands of Argentina.

VALUES AND LIFE SKILLS

We must learn not to exploit natural resources and to instead, take care of our environment and the natural resources we have, like the indigenous people in the Amazon Basin

The Natural vegetation largely depends on climate,soil and the relief features.North America has a wide variety of vegetation. These vegetation belts follow the climatic zones.

Tundra Type  vegetation
In the northern parts of Canada This type of vegetation is found.  Mosses, Lichen and dwarf willows grow. There is not much growth of vegetation only some bright flowering plants grown in short  summer season.

The Coniferous  forests
To the south of Tundra belt in southern Canada lies the Coniferous  forests. These forests consist of trees like pine, spruce and fir. Trees of this region have conical leaves and thick stem.

The Temperate Mixed  forests
Oak, Beach, Dauglas fir and Maple trees are examples of the Temperate Mixed Forests vegetation in Canada and USA. Most of the soft wood industries of Canada are developed in this region.

The Temperate Grasslands
The Temperate Grasslands Of North America are called as Prairies. Only grass grows due to less amount of rainfall. Tall trees are almost absent.

 The Mediterranean Type
The trees of this region are small with shininig leaves and hard stem. Olive, cork, myrtle and oak are the main trees found here alomg with Fruit tree like Oranges, Grapes, Apricots.

The Dry Forests
These forests are also called as Desert Vegetation. In this region hardly any forests are available due to extreme climate and low rainfall. Cactus, thorny bushes are the main vegetation here.

The Tropical rain forests
These forests are around the gulf of Mexico coastal region. The main trees found in this region are palm, Yellow Pine and Cypress. Most of the land of this region is under cultivation.

Warm Temperate forests
These forests  are of mixed coniferous and deciduous foresets. This region consist of the treee like  Oak, Chestnut, Magnolia, Yellow Pine  and Cypress. Yellow Pine trees are very famous in this region.

MINERAL AND POWER RESOURCES

Coal

• Pennsylvanian Anthracite
• Appalachian Bituminous
• Pittsburgh N. Appalachians (Iron and steel Capital of the world)
• Birmingham S. Appalachians (Pittsburgh of the south)
• Interior Provinces (Indiana, Illinois, Iowa, Missouri, Kansas, Oklahoma, Arkansas)
• Gulf Provinces (Texas, Alabama, Arkansas)
• Rocky Mountain Provinces (Utah, Colorado, Wyoming, Montana, N. Mexico, N. Dakota)
• Pacific Provinces (Washington, Oregon, California)
• Alaska (future reserves)

Hydro Electric Project (HEP)

Fall Line (Appalachians) , Rockies, Mississippi Basin, Laurentian Shield, Great Lakes, St. Lawrence, Grand coulee Dam , R. Columbia (Washington) , Bonneville Dam R. Columbia (Washington) , Hoover Dam or Boulder Dam (reservoir L. Mead) R . Colorado, Davis Dam and Parker Dam (R. Colorado in Arizona) , St. Lawrence Seaway with generating stations at Beauharnais, Cornwall, Prescott, Kingston, Montreal, St. Anthony falls (Minneapolis) , Long Sault Rapids (Massena) . Dams along Mississippi and Missouri (Fort peck, Garrison, Fort Randall, Gavin՚s Point) . Tennessee Valley Project on R. Tennessee.

Petroleum and Natural Gas

1. Midcontinental region (Texas, Oklahoma and Kansas)

1. 1930 Oklahoma City became the heart of American oil industry.
2. Also a great Natural gas area.

2. Gulf coasts region

1. (S. Texas, Louisiana, Mississippi and Arkansas)
2. Extends under the continental shelf of the Gulf of Mexico.

3. Rocky Mountain Regions

1. Wyoming, Colorado, Montana, N Mexico
2. Mining difficult and expensive (because of scattered deposits, folding and faulting)

4. Californian Region: Centered at Los Angeles, Long Beach and S San Joaquin

5. Appalachian and Eastern Interior Region (Pennsylvania, Kentucky and Ohio

6. Alaska Region (A pipeline for shipment to USA From Alaska to Valdez)

Iron Ore

• Lake Superior region (Hematite) e. g. Mesabi (Iron ore is shipped from Duluth)
• North East region Adirondacks (New York) and Cornwall (Pennsylvania)
• South East region Birmingham (Alabama) (Red Mountains)
• Western region Scattered fields at Utah (Iron Mountain) , Nevada, Wyoming, California (Eagle Mountain) Steelworks at San Francisco Los Angeles Pueblo (Colorado) Provo (Utah) Copper
  • Arizona Globe Morenci Largest single copper mine Bingham (Utah) -Montana Butte
  • Nevada and New Mexico (new Producers)

Tin

• USA is very short of tin and therefore imports and stockpiles large quantities. -American stockpile release drastically affects tin prices Bauxite
• Due to great bulk of the Bauxite, concentration is due at seaboard Locations. -Mobile (Alabama) -Baton Rouge (Louisiana)

Others

• Lead Rockies, Ozark Plateau of Missouri, Idaho, Utah, Arizona, and Colorado.
• Zinc Missouri, Oklahoma, Kansas
• Tungsten Nevada, Utah, Idaho
• Molybdenum Leading producer. Climax mine of Colorado is probably the world՚s largest molybdenum mine.
• Platinum California
• Mica Largest produces are Eastern Rockies and Appalachians
• Sulphur Texas (major producer)
• Silver, Vanadium and Uranium are also found.

Industrial Regions

Southern New England

• Centered at Boston -Boston (Shipbuilding, Textiles, Shoemaking, Footwear Machinery)
• Lowell Providence (Woolen Textile)
• New Bedford (Worsted Textiles)
• Fall River (Cotton Textiles) -Hartford (Aircraft and Armaments)

Mid Atlantic States

• Depends upon Pennsylvanian anthracite Iron ore, Coal and oil from Appalachians (Industrial conurbation from New York to Baltimore) Iron and Steel industries, Engineering, electrical goods etc. Pittsburgh Lake Erie region -Iron and steel Region
• Pittsburgh (Iron Steel capital of the world) , Cleveland (Steel, Wearing apparel) , Wheeling (Steel) , Akron (Rubber) , East Liverpool (Pottery) , Buffalo (Flour milling chemical metal goods)

Detroit Region

• Detroit Greatest automobile manufacturing region
• Centered at Detroit, Lansing and Toledo Automobile and related industries

Lake Michigan Region

• Chicago (Focal point at the convergence of roads and railways from all over the USA) Iron and Steel, Meat Packing, Grain milling, Agricultural machines, Rail Engines and coaches
• Milwaukee Steel Engineering Textiles -Gary Iron and Steel

Southern Appalachian Region

• Birmingham Iron and Steel. (The region gets its H. E. P from the Appalachian fall line) .

Eastern Texas

• Industrial development dependent upon oil. The area has world՚s largest known deposits of Sulphur.
• Known for Oil, Chemical and cotton Industries.
• Shift westward of cotton belt has provided raw material and Created markets.
• Assisted by the construction of Intra coastal waterway running parallel to the coast.
• Houston Oil refineries, chemical plants, synthetic rubber
• Dallas and Fort Worth are twin cities lying in this region. Dallas, a major cotton market is known for clothing and fashion. Fort Worth is known for Cattle, aircraft and aerospace. These two cities share the world՚s largest airport and are also major financial centers owing to vast oil wealth.

Other Industrial Cities

• St Louis Meat Packing, Flour Milling and Agricultural machines
• Kansas City Agricultural machine, Aircraft, Oil refining
• Omaha, Cincinnati, Indianapolis, Denver, St. Paul, Minneapolis, and Memphis these places have Flour milling, Meat packing, Cotton textiles, Food processing and other agricultural industries.
• New Orleans Oil refining, Chemicals and Cotton textiles -San Francisco Oil refining, steel, aircraft engineering, food processing.
• Los Angeles and San Diego -Oil refining, steel, aircraft engineering, food processing, television
• Seattle Aircraft, Lumbering, Fish Canning, aluminum smelting.

Canada

Coal

Cape Breton Island, Vancouver Island (Lies in British Columbia and feeds the Sydney Steel Plants) and Alberta.

Hydro-Electirc Projects

• Vancouver, Duncan, Bridge river, Arrow Lakes, Corner Brook, Kemono, Churchill falls (formerly Hamilton falls) .
• St. Lawrence Niagara falls -Rapids at Salt Ste Marie -Nipigon River (Port Arthur and Fort William)
• Winnipeg River -Kitimat scheme (R. Nechaka) Petroleum
• Prairie provinces of Alberta and Saskatchewan (centered at Edmonton, Calgary and Turner valley) , Grand Bank, Athabasca Tar Sand.
• Trans Canadian gas pipeline supplies gas from Alberta gas fields to Toronto and Montreal. Iron Ore
• Knob Lake (Labrador) , Steep Rock (N. of Lake Superior) Baffin Island

Others

• Copper Sudbury, Flin Flon, Sheridan, Lynn Lake and Coppermine
• Nickel Sudbury, Lynn Lake, Hope, Thompson
• Lead, Zinc and Silver Sullivan Mines (British Columbia) . Also in Manitoba and North

West Territories Industries

1. Lake Peninsula to Montreal -Good Accessibility, Cheap H. E. P American investment Toronto Engineering, Automobile, Chemicals, Textiles, Pulping and Food processing Hamilton (Birmingham of Canada) Heavy engineering and Iron and Steel. Windsor Automobile, Tyre making- Kingston Locomotive
2. St. Lawrence region Montreal Ship Building, Oil Refining, Paper and Pulp and Food Processing. It is a Leading Grain port. Quebec Marine Engineering, Ship building, Food Processing Ottawa Saw milling, Paper and Pulp
3. Continental interior (Canadian Prairie) Winnipeg Agricultural, industries, Fur, Dressing textiles Edmonton Oil extraction, Natural gas
4. Vancouver Lumbering Timber industries Fish canning

POINTS TO REMEMBER

• North America has been named after Amerigo Vespucci, an Italian explorer. However, Christopher Columbus is credited with the discovery of this continent.
• The continent lies in the northern and the western hemispheres surrounded by the Arctic, the Atlantic and the Pacific oceans. The Isthmus of Panama joins North America to South America.
• The United States of America and Canada occupy three fourths of North america.
• NorthAmerica can be divided into four major physical divisions— the Canadian or Laurentian Shield, the Western Mountain System or Western Cordilleras, the Eastern Highlands or Appalachian Mountains and the Central Lowlands or Great Central Plains.
• The Canadian Shield is composed of some of the oldest known hard rocks of the world. The surface of the Shield consists of many deep depressions formed by scraping and scouring out by moving ice. These depressions have been filled up with meltwater to form many freshwater lakes such as the five Great Lakes.
• The Western Cordilleras are a series of young fold mountain ranges which have many active and extinct volcanoes, earthquake-prone regions and hot springs. The Cordilleras consist of several parallel ranges such as the Alaska Range and the Brooks Range. The highest point in North America, Mt McKinley, lies here. .
• The Appalachians are lower than the Western Cordilleras. The eastern slopes of these highlands are very steep.
• The edge of the Piedmont Plateau (located at the foot of the Appalachians or the Eastern Highlands) has many waterfalls along its length. It is referred to as the Fall Line.
• The Great Central Plains have the largest river system in North America—the Mississippi-Missouri river system.
• North America has several large rivers such as the Mississippi, Missouri, Mackenzie, Nelson, St Lawrence, Hudson, Yukon, Columbia and Rio Grande.
• Lumbering is an important activity in the coniferous or taiga forests of Canada, carried out by lumbermen or lumberjacks.
• Lumbering involves several stages of work such as cutting, skidding and hauling.

IMPORTANT TERMS

Gorge : A deep narrow valley with near vertical sides. Intermontane plateau: a plateau surrounded by mountains on all sides.
Lumbering : The cutting down of trees and the processes leading to the manufacture of products like paper, newsprint, synthetic fibres, etc.
Lumberjacks : Workers engaged in lumbering.
Meltwater : Water derived from the melting of glacier ice and/or snow.

VALUES AND LIFE SKILLS

All occupations are important. Every job has dignity and deserves our respect.

POINTS TO REMEMBER

• The climate of South America is influenced by its location, presence of the Andes Mountains, prevailing winds, nearness to seas and oceans, and the impact of ocean currents.
• The vast continent of South America has a climate that varies from the equatorial climate in most of Brazil, to the desert climate of the Atacama and Patagonian Deserts.
• Some areas of Venezuela, Guyana, and Brazil also experience tropical climate. There is a small stretch of central Chile which experiences Mediterranean climate. Southern Chile has a maritime climate.
• Different climates have influenced the natural vegetation found in South America. Forests exist in areas that receive heavy rainfall throughout the year such as the equatorial forests of the Amazon Basin. Grasslands predominate in regions that record maximum rainfall during the summers such as the grasslands in Guyana and Brazil. Deserts exist in areas that receive hardly any rainfall such as the Atacama and Patagonian Deserts. Mountain vegetation grows in the Andes and Mediterranean vegetation is found in central Chile.
• The wildlife of South America includes several unusual species such as the anaconda, birds such as the egret, rhea, and condor, and animals such as the guanaco, vicuna, and llama.
• Hardwood trees like mahogany, rosewood, and rubber are found in the selvas. Brazil nuts, balsa, cinchona for quinine, gum, resins, and dyes are other products obtained from these forests. Yerba mate is an important tree that grows in the Eastern Highlands.
• Rivers like the Amazon, Orinoco, and Parana provide inland water transport. Brazil, Argentina, Paraguay, and Venezuela have developed hydroelectric power projects.
• South America is rich in minerals ranging from crude oil, copper, diamond, gold to silver. This is what attracted the Europeans to settle in this continent.

IMPORTANT TERMS

Campos : the tropical grasslands in central Brazil.
Gran Chaco : lowland alluvial plain in interior south-central South America.
Armadillo : an animal found in South America with a hard shell made of pieces-Of bone.
Lguana : a large tropical lizard found in South America

Chemistry is a fascinating science, full of unusual trivia. Chemistry is indeed in our everyday life. We find chemistry in the food we eat, the air we breathe, cleaning products, our emotions and literally every object we can see or touch.

Chemists use all kinds of equipment in their labs to run their experiments. In this topic, you will see some of the most common pieces of equipment and their uses and also precautions to be taken in the chemistry lab.

When performing experiments, taking accurate measurements is crucial. There are a wide variety of measurements that can be taken depending on the task at hand. 

In this chapter, you will find a table which contains images of basic apparatus and how to use each piece of equipment in the laboratories.

Common laboratory apparatus and equipment

We must use our everyday experiences to understand various natural phenomena. In living beings, observation employs the senses. In science, observation can also involve the recording of data using instruments. It also refers to any data collected during the scientific activity. Careful observations help us to draw scientific conclusions.

 A chemistry laboratory helps students to:

• Observe and see for themselves.
• Understand the difference between different compounds.
• Learn the importance of observation and experiment.

Precautions to be taken in the chemistry lab

Safety is a key concern in any scientific enterprise, but particularly in the chemistry laboratory. There are many potential hazards when working with chemicals, but all of them can be avoided with the appropriate precautions.

• Always wear an apron to protect your clothes.
• Never work alone with chemicals.
• Never touch or taste any substance.
• Use small quantities of substances.
• While heating substances, stand away from the burner and hold the tube away from yourself to avoid splashing.
• Arrange apparatus and reagents in an orderly manner before starting the experiment

Types of Farming

The cultivation methods depend upon the characteristics of the physical environment, technological know-how and socio-cultural practices. Farming varies from subsistence to commercial type. In different parts of India, the following farming systems are practised.

Primitive Subsistence Farming

It is a ‘slash and burn’ agriculture. Farmers clear a patch of land and produce cereals and other food crops. When the soil fertility decreases, the farmers shift and clear a fresh patch of land for cultivation. It is known by different names in different parts of the country. It is known as jhumming in north-eastern states.

• Land productivity is low in this type of agriculture.
• This type of farming depends on monsoon.
• This farming is practised in a few parts of India.

Intensive Subsistence Farming

• This type of farming is practised in areas of high population pressure on land.
• It is labour-intensive farming, where high doses of biochemical inputs and irrigation are used for higher production.

Commercial Farming

This type of farming uses higher doses of modern inputs such as high yielding variety (HYV) seeds, chemical fertilisers, insecticides and pesticides to obtain higher productivity.

Plantation is a type of commercial farming in which a single crop is grown on a large area. Plantations cover large tracts of land, using capital intensive inputs, with the help of migrant labourers. All the produce is used as a raw material in industries.

Eg: Tea, Coffee, Rubber, Sugarcane, Banana.

Cropping Pattern

India has three cropping seasons:

1. Rabi
2. Kharif
3. Zaid

	Rabi	Kharif	Zaid
Sowing Season	Winter from October to December	Beginning of the rainy season between April and May	In between the Rabi and the Kharif seasons, there is a short season during the summer months known as the Zaid season (in the months of March to July)
Harvesting Season	Summer fromApril to June	September-October
Important Crops	Wheat, Barley, Peas, Gram and Mustard.	Paddy, Maize, Jowar, Bajra, Tur (Arhar),Moong, Urad, Cotton, Jute, Groundnut andSoyabean.	Watermelon, Muskmelon, Cucumber,Vegetables and Fodder crops

Major Crops in India

A variety of food and non-food crops are grown in different parts of India, depending upon the variations in soil, climate and cultivation practices. Major crops grown in India are:

• Rice
• Wheat
• Millets
• Pulses
• Tea
• Coffee
• Sugarcane
• oil seeds
• Cotton
• Jute

We will discuss all of these one by one, in detail.

Rice

1. It is a kharif crop.
2. It requires high temperature and high humidity with annual rainfall above 100 cm.
3. India is the second largest producer of rice in the world after China.
4. It is grown in the plains of north and north-eastern India, coastal areas and the deltaic regions.

Wheat

1. This is a rabi crop.
2. It requires a cool growing season and bright sunshine at the time of ripening.
3. It requires 50 to 75 cm of annual rainfall evenly distributed over the growing season.
4. The Ganga-Satluj plains in the north-west and black soil region of the Deccan are two main wheat-growing zones in India.
5. It is the second most important cereal crop and main food crop, in the north and north-western part of India.

Millets

1. Jowar, Bajra and Ragi are the important millets grown in India.
2. These are known as coarse grains and have very high nutritional value.

Jowar	Bajra	Ragi
3rd most important food crop with respect to area and production.	Grows well on sandy soils and shallow black soil.	It is a crop of dry regions.
It is a rain-fed crop mostly grown in the moist areas.	Grows well on red, black, sandy, loamy and shallow black soils.
Mainly produced in Maharashtra, Karnataka, Andhra Pradesh and Madhya Pradesh.	Major producing states are Rajasthan, Uttar Pradesh, Maharashtra, Gujarat and Haryana.	Major producing states are Karnataka, Tamil Nadu, Himachal Pradesh, Uttarakhand, Sikkim, Jharkhand and Arunachal Pradesh.

Maize

1. It is a Kharif crop.
2. It requires temperature between 21°C to 27°C and grows well in old alluvial soil.
3. It is used both as food and fodder.
4. Major maize-producing states are Karnataka, Madhya Pradesh, Uttar Pradesh, Bihar, Andhra Pradesh and Telangana.

Pulses

1. India is the largest producer and consumer of pulses in the world.
2. Pulses are the major source of protein in a vegetarian diet.
3. Major pulses grown in India are Tur (Arhar), Urad, Moong, Masur, Peas and Gram.
4. Pulses are mostly grown in rotation with other crops so that the soil restores fertility.
5. Major pulse producing states are Madhya Pradesh, Rajasthan, Maharashtra, Uttar Pradesh and Karnataka.

Food Crops other than Grains

Sugarcane

1. It is a tropical as well as a subtropical crop.
2. It grows well in hot and humid climates with a temperature of 21°C to 27°C and annual rainfall between 75cm to 100cm.
3. It can be grown on a variety of soils.
4. Needs manual labour from sowing to harvesting.
5. India is the second largest producer of sugarcane only after Brazil.
6. Sugarcane is the main source of Sugar, Gur (Jaggery), Khansari and molasses.
7. The major sugarcane-producing states are Uttar Pradesh, Maharashtra, Karnataka, Tamil Nadu, Andhra Pradesh, Telangana, Bihar, Punjab and Haryana.

Oil Seeds

Different oil seeds are grown covering approximately 12% of the total cropped area of India. Main oil-seeds produced in India are:

• Groundnut: is a Kharif crop and accounts for half of the major oilseeds produced in India. Gujarat is the largest producer of groundnuts.
• Mustard: is a rabi crop.
• Sesamum (til): is a Kharif crop in the north and rabi crop in south India.
• Castor seeds: It is grown as both Rabi and Kharif crop.
• Linseed: is a rabi crop.
• Coconut
• Soyabean
• Cotton seeds
• Sunflower

Tea

1. It is also an important beverage crop introduced by the British in India.
2. The tea plant grows well in tropical and sub-tropical climates with deep and fertile well-drained soil, rich in humus and organic matter.
3. Tea bushes require warm and moist frost-free climate all through the year.
4. Tea is a labour-intensive industry.
5. Major tea producing states are Assam, hills of Darjeeling and Jalpaiguri districts, West Bengal, Tamil Nadu and Kerala.

Coffee

Yemen coffee is produced in India and this variety of coffee is in great demand all over the world. Its cultivation was introduced on the Baba Budan Hills and is confined to the Nilgiri in Karnataka, Kerala and Tamil Nadu.

Horticulture Crops

India is a producer of tropical as well as temperate fruits. Major crops produced are pea, cauliflower, onion, cabbage, tomato, brinjal and potato. Some of the famous horticulture crops grown in India are:

• Mangoes of Maharashtra, Andhra Pradesh, Telangana, Uttar Pradesh and West Bengal Oranges of Nagpur and Cherrapunjee (Meghalaya), bananas of Kerala, Mizoram, Maharashtra and Tamil Nadu.
• Lichi and Guava of Uttar Pradesh and Bihar
• Pineapples of Meghalaya
• Grapes of Andhra Pradesh, Telangana and Maharashtra
• Apples, pears, apricots and walnuts of Jammu and Kashmir and Himachal Pradesh

Non-Food Crops

Rubber	Fibre	Cotton	Jute
It is an equatorial crop.	Cotton, Jute, Hemp and Natural Silk are the four major fibre crops.	It is a Kharif crop.	It is known as the golden fibre.
It requires a moist and humid climate with rainfall of more than 200cm and temperature above 25°C.	Cotton, Jute and Hemp are grown in the soil.	It requires hightemperature, light rainfall, 210 frost-free days and bright sunshine for its growth.	It grows well on well-drained fertile soils in the flood plains. High temperature is required for its growth.
It is an important industrial raw material	Natural Silk is obtained from cocoons of the silkworms fed on green leaves	Cotton growswell in black cotton soil of the Deccan plateau.	It is used in making gunny bags, mats, ropes, yarn, carpets and other artefacts.
Mainly grown in Kerala, Tamil Nadu, Karnataka and Andaman and Nicobar islands and Garo hills of Meghalaya.	Rearing of silkworms for the production of silk fibre is known asSericulture.	Major cotton-producing states are Maharashtra, Gujarat, Madhya Pradesh, Karnataka, Andhra Pradesh,Telangana, Tamil Nadu, Punjab, Haryana andUttar Pradesh.	Major jute producing states are West Bengal, Bihar, Assam, Odisha and Meghalaya.

Technological and Institutional Reforms

Agriculture provides a livelihood for more than 60% of its population, so this sector needs some serious technical and institutional reforms. The Green Revolution and the White Revolution were some of the reforms initiated by people to improve agriculture.

Some Initiatives taken by the Government are:

• Schemes introduced by Government such as Kissan Credit Card (KCC), Personal Accident Insurance Scheme (PAIS).
• Special weather bulletins and agricultural programmes for farmers on the radio and television were introduced.
• The government also announces minimum support price, remunerative and procurement prices for important crops to check the exploitation of farmers by speculators and middlemen.

Contribution of Agriculture to the National Economy, Employment and Output

• In 2010-11 about 52% of the total workforce was employed by the farm sector.
• The share of agriculture in the GDP is declining.
• Indian Council of Agricultural Research (ICAR), agricultural universities, veterinary services and animal breeding centres, horticulture development, research and development in the field of meteorology and weather forecast, etc. are a few of the initiatives introduced by the government to improve Indian agriculture.