Equivalent Fractions have the same value, even though they may look different. These fractions are really the same.

For example,

3/4 = 6/8 = 12/16

Why are they the same ?

Because when we multiply or divide both the numerator and denominator by the same number, the fraction keeps it's value.

Let us divide a rectangle into two equal parts and shade one part.

In the above rectangle, the shaded part is 1/2.

That is, in total of 2 parts, one part is shaded.

Let us divide the same rectangle into four equal parts and shade 2 parts.

In the above rectangle, the shaded part is 2/4.

That is, in total of 4 parts, two parts are shaded.

Let us divide the same rectangle into six equal parts and shade 3 parts.

In the above rectangle, the shaded part is 3/6.

That is, in total of 6 parts, three parts are shaded.

In all the above figures, the shaded portion are equal but they can be represented by different fractions.

1/2 = 2/4 = 3//6

When two or more fractions represent the same part of a whole, the fractions are called equivalent.

**Rule to get equivalent fractions : **

Change both numerator and denominator using multiplication or division.

**Examples : **

Using multiplication

1/2, 2/4 and 4/8 are equivalent fractions.

Using division

18/36, 6/12 and 1/2 are equivalent fractions.

**Problem 1 :**

Write 4 fractions which are equivalent to 5/6.

**Solution : **

5/6 = (5x2)/(6x2) = 10/12

10/12 = (10x2)/(12x2) = 20/24

20/24 = (20x2)/(24x2) = 40/48

40/48 = (40x2)/(48x2) = 80/96

The four fractions which are equivalent to 5/6 are

10/12, 20/24, 40/48 and 80/96

**Problem 2 :**

Write 3 fractions which are equivalent to 3/7.

**Solution : **

3/7 = (3x2)/(7x2) = 6/14

6/14 = (6x2)/(14x2) = 12/28

12/28 = (12x2)/(28x2) = 24/56

The three fractions which are equivalent to 3/7 are

6/14, 12/28 and 24/56

**Problem 3 :**

Pick out the fractions which are equivalent :

2/5, 12/16, 1/3, 5/15, 16/40, 3/4, 9/12

**Solution : **

**The fractions 2/5 and 16/40 are equivalent. **

Because, 2/5 = (2x8) / (5x8) = 16/40

**The fractions 12/16, 3/4 and 9/12 are equivalent.**

Because, 12/16 = (12÷4) / (16÷4) = 3/4

and 9/12 = (9÷3) / (12÷3) = 3/4

**The fractions 1/3 and 5/15 are equivalent. **

Because, 1/3 = (1x5) / (3x5) = 5/15

**Problem 4 : **

Find the missing number :

The numerator of the first two fractions are 5 and 35. And 5 will become 35, when we multiply by 7.

So, we have to multiply the denominator of the first fraction 9 by 7 in order to get the denominator of the second fraction.

**Hence, the denominator of the second fraction is 63.**

The denominator of the first and third fraction are 9 and 72. And 9 will become 72, when we multiply by 8.

So, we have to multiply the numerator of the first fraction 5 by 8 in order to get the numerator of the third fraction.

**Hence, the numerator of the third fraction is 40.**

That is,

**Problem 5 :**

Find the missing number :

The numerator of the first two fractions are 3 and 21. And 3 will become 21, when we multiply by 7.

So, we have to multiply the denominator of the first fraction 5 by 7 in order to get the denominator of the second fraction.

**Hence, the denominator of the second fraction is 35.**

The denominator of the first and third fraction are 5 and 20. And 5 will become 20, when we multiply by 4.

So, we have to multiply the numerator of the first fraction 3 by 4 in order to get the numerator of the third fraction.

**Hence, the numerator of the third fraction is 12.**

That is,

After having gone through the stuff given above, we hope that the students would have understood "Equivalent-fractions".

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