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# Equivalent Fractions

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Look at the images given below. What do the fractions in the images have in common?

Each fraction in the image represents the same value. These fractions are equivalent.

## Equivalent Fractions

Equivalent fractions are fractions that have different numbers but the same value.

The fractions
1
2
,
2
4
,
3
6
,
4
8
are equivalent since each represents the same value

One way to tell if two fractions are equivalent is to draw a picture.

Let's use a picture to decide if
2
3
and
4
6
are equivalent.

First of all draw 2 boxes and label them: Now divide each box. The first box has a denominator of 3, so split it into 3 sections. The second box has a denominator of 6, split that into 6 sections. Next color these boxes using the numerators. The first fraction has a numerator of 2, so color 2 boxes. The second has a numerator of 4, color 4 boxes. We notice that the same amount of each box is colored, so, these are equivalent fractions.  ## Arithmetic Procedure of Finding Equivalent Fractions

To find equivalent fractions, multiply or divide the numerator and denominator by the same number.

Let's illustrate through an example.

### Example 1

Are
1
2
and
3
6
equivalent?

To check if two fractions are equivalent multiply or divide by the same number.

We notice that
1
2
is already in the simplest form. So, we can't reduce it further.
Reduce
3
6
by dividing it by 3.

3 ÷ 3
6 ÷ 3
=
1
2

Both fractions reduces to
1
2
, so they are equivalent.

### Example 2

Find two fractions that are equivalent to
2
3
.
To find the equivalent fractions of
2
3
, multiply numerator and denominator by the same number.

Multiply numerator and denominator by 2.

2 x 2
3 x 2
=
4
6

To find another equivalent fraction of
2
3
, multiply numerator and denominator by 3.

2 x 3
3 x 3
=
6
9

So,
4
6
and
6
9
are equivalent fractions of
2
3
.

### Example 3

Find the missing number that makes the fraction equivalent.
3
5
=
---
20

To find the missing number, look at the denominator.

In denominator, 5 is multiplied by 4 to get 20.

So, multiply the numerator 3 by the same number 4 to find the missing number.

3 x 4
5 x 4
=
12
20

3
5
is equivalent to
12
20
.
Summary
• Equivalent fractions are fractions that have different numbers but the same value.
• We can use pictures to check if two fractions are equivalent.
• To find equivalent fractions, multiply or divide the numerator and denominator by the same number.
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