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# Class 7 Fractions

Introduction to Fractions

Types of Fractions

Decimal Fraction

Vulgar Fraction

Proper Fraction

Improper Fraction

Mixed Fraction

Like Fraction

Unlike fractions

Equivalent fractions

Irreducible fraction

Comparison of more than two fractions

Subtraction of Like Fraction

Subtraction of Unlike Fraction

Multiplication of Fraction

Reciprocal of Fraction

Division of Fractions

Fractions Test

Fractions Worksheet

## Introduction to Fractions

The numbers having ab are known as fractions. Here 'a' is known as numerator and 'b' is known as denominator.

## Types of Fractions

1. Decimal fraction
2. Vulgar fraction
3. Proper fraction
4. Proper fraction
5. Improper fraction
6. Mixed fraction
7. Like fractions
8. Unlike fractions
9. Equivalent fractions
10. Irreducible fraction

## Decimal Fraction

Fraction whose denominator is either 10, 100, 1000, etc. ... are known as decimal fraction. Few decimal fractions are shown below.

710, 9100, 11100

## Vulgar Fraction

A fraction whose denominator is a whole number other than 10, 100, 1000 etc. is known as vulgar fraction.

27, 59, 713, 920, etc... all are vulgar fractions.

## Proper Fraction

Fraction whose numerator is less than the denominator is known as proper fraction. Few examples are given below.

25, 34, 59, 917, etc...

## Improper Fraction

Fraction whose numerator is more than or equal to its denominator is known as improper fraction. Few examples are given below.

53, 95, 107, 2523. Etc...

## Mixed Fraction

A number which can be expressed as the sum of a natural number and a proper fraction is known as a mixed fraction. Few examples are given below.

123, 235, 357, etc...

## Like Fraction

Fraction having same denominator, but different numerators are known as like fractions. Let's see some example.

512, 712, 1112 are like fractions.

## Unlike fractions

Fractions having different denominators are known as unlike fractions. Let's see some example.

25, 57, 911, etc...

## Equivalent fractions

If a given fraction's numerator and denominator is multiplied or divided by same nonzero number then the resultant fraction will be known as equivalent fraction. Let's see some examples.

23, 46, 812, 1624, etc... are all equivalent fractions.

## Irreducible fraction

A fraction is said to be irreducible form, if HCF of it's numerator and denominator is 1. If HCF of numerator and denominator is other than 1 then the fraction is known as reducible.

Example 1. Convert 4563 into irreducible form.

Solution. First we must find the HCF of 45 and 63.

HCF of 45 and 63 is 9.

Let's divide the numerator and denominator by 9.

4563 = (45÷9)(63÷9) = 57

Hence, 4563 irreducible form is 57.

## Comparison of more than two fractions

Step 1. Find the LCM of the denominators of the given fraction.

Step 2. Convert all the given fractions into like fractions in such a way that all the fraction's denominator should be LCM.

Step 3. Compare any two of these like fractions, one having larger numerator is larger among the two fractions.

Example 1. Arrange the below given fractions in ascending order.
710, 1315, 35

Solution. The given fractions are 710, 1315, 35.

LCM of 5, 10, and 15 = 60

Now, let us change each of the given fractions into an equivalent fraction having 60 as their denominator.

710 = (7x6)(10x6) = 4260

1315 = (13x4)(15x4) = 5260

35 = (3x12)(5x12) = 3660

So, 3660 < 4260 < 5260

Hence, the given fractions in ascending order are 35, 710, 1315.

For adding two like fractions, the numerators are added and the denominator remains the same. Let's see some examples.

Example 1. Add 27 and 37.

Solution. 27 + 37 = (2+3)7= 57

Example 2. Add 415 and 715.

Solution. 415 + 715 = (4+7)15 = 1115

For addition of two unlike fractions, first change them to like fractions and then add them as like fractions. Let's see some examples.

Example 1. Add 35 and 715.

Solution. 35 + 715

LCM of 5 and 15 is 15.

Now, convert 35 and 715 into like fractions.

35 = (3x3)(5x3) = 915

915 and 715 are like fractions.

915 + 715 = (9+7)15 = 1615

1. Commutative
2. Associative

### Commutative

Addition of fraction is commutative, that is ab + cd = cd + ab

### Associative

Addition of fraction is associative, that is (ab + cd) + ef = ab + (cd + ef)

## Subtraction of Like Fraction

Subtraction of like fractions can be performed in a manner similar to that of addition. Let's see some example.

Example 1. Subtract 1115 from 1315.

Solution. 13151115 = (13−11)15 = 215

Example 2. Subtract 1537 from 2237.

Solution. 22371537 = (22−15)37 = 737

## Subtraction of Unlike Fraction

Subtraction of unlike fractions can be performed in a manner similar to that of subtraction. Let's see some example.

Example 1. Subtract 720 from 1315.

Solution. 1315720

LCM of 15 and 20 = 60

Convert both the fraction to equivalent fraction having denominator 60.

1315 = (13x4)(15x4) = 5260

720 = (7x3)(20x3) = 2160

Now, subtract both the equivalent fractions.

52602160 = (52−21)60 = 3160

Example 2. What should be added to 1223 to get 1556?

Solution. 1556 − 1223 = 956383

LCM of 6 and 3 = 6

Now, convert 956 and 383 into equivalent fraction having denominator 6.

383 = (38x2)(3x2) = 766

956766 = (95−76)6 = 196

## Multiplication of Fraction

Product of two fractions is equal to product of their numerators and product of their denominators. Let's see some examples.

Example 1. Multiply 57 and 34.

Solution. 57 x 34 = (5x3)(7x4) = 1528

Example 2. Multiply 1023 and 215.

Solution. First, we must convert both the mixed fractions to improper fractions.

1023 = 323

215 = 115

Now, multiply both the improper fractions.

323 x 115 = (32x11)(3x5) = 35215 = 23715

Example 3. 25 of 20.

Solution. 25 x 20 = (2x20)5 = 405 = 8

Example 4. John can walk 235 km per hour. How much distance will he cover in 213 hours?

Solution. Distance covered by John in one hour = 235 = 135

Distance covered by John in 213 hours = 135 x 73 = 9115 = 6115

So, John will cover 6115 km in 213 hours.

## Reciprocal of Fraction

Two fractions are said to be reciprocal of each other, if their product is 1. In other words, if ab is a fraction, then ba is it's reciprocal. Let's see some examples.

Example 1. Find the reciprocal of 57.

Solution. Reciprocal of 57 is 75.

Example 2. Find the reciprocal of 235.

Solution. 235 = 135

Reciprocal of 135 is 513.

## Division of Fractions

To divide a fraction by another fraction, the first fraction is multiplied by the reciprocal of the second fraction.

ab ÷ cd = ab x dc

Example 1. Divide 59 by 15.

Solution. 59 ÷ 15 = 59 x 115 = 127

Example 2. Divide 535 by 3110.

Solution. 535 ÷ 3110
285 ÷ 3110 = 285 x 1031 = 5631

Example 3. Divide 35 by 54.

Solution. 35 ÷ 54 = 35 x 45 = 7 x 4 = 28

Example 4. Cost of 235 kg orange is Rs. 260. What is the cost of 1 kg orange?

Solution. Cost of 135 kg orange = Rs. 260

Cost of 1 kg orange = 260 ÷ 135

= 260 x 513 = 100

Hence, cost of 1 kg orange is Rs. 100.

## Class-7 Fractions Test

Fractions Test - 1

Fractions Test - 2

## Class-7 Fractions Worksheet

Fractions Worksheet - 1

Fractions Worksheet - 2

Fractions Worksheet - 3

Fractions Worksheet - 4