Equivalent Fractions
Definition
In arithmetic, an equivalent fraction is a fraction with the different numerator and the denominator but represents the simplified value of that fraction or proportion (part) of the whole.
In other words, equivalent fractions are different fractions that we get after simplification of the fraction or after multiplying by the same number in numerator and denominator.
For example, 
is equal to 
. Hence, is an equivalent fraction of . Similarly, 
is also an equivalent fraction of .
How to Find Equivalent Fractions
There are two ways to find the equivalent fractions:
- Using Multiplication
- Using Division
Using Multiplication
It is used when the fraction is in its simplest form. We multiply the numerator and denominator by the same number to get the equivalent fractions.
For example, the equivalent fractions of 
are:
In the fraction , we have multiplied the numerator and the denominator by 3 to get the equivalent fraction.
In the fraction , we have multiplied the numerator and the denominator by 6 to get the equivalent fraction. Similarly, we can find more equivalent fractions of .
Using Division
It is used when the fraction is not in the simplest form. We divide the numerator and denominator by the same number to get the equivalent fractions.
For example, the equivalent fractions of 
are:
In the above example, we have divided the fraction by 2, to get the equivalent fractions. We have done this process until we get the simplest form of the fraction. The fractions that we get during the simplification are called equivalent fractions.
Note: Never add or subtract the fractions to get the equivalent fractions. All equivalent fractions reduce to the same fraction in their simplest form. To get the equivalent fraction, it is not necessary to simplify the fraction in the simplest form.
Equivalent Fractions Chart
In the following chart, we have covered some fractions equivalent that can help to simplify the fraction.
| Fraction | Equivalent Fractions | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 | 6/12 | 7/14 | 8/16 | 9/18 | 10/20 | 11/22 | 12/24 |
| 1/3 | 2/6 | 3/9 | 4/12 | 5/15 | 6/18 | 7/21 | 8/24 | 9/27 | 10/30 | 11/33 | 12/36 |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 | 12/18 | 14/21 | 16/24 | 18/27 | 20/30 | 22/33 | 24/36 |
| 1/4 | 2/8 | 3/12 | 4/16 | 5/20 | 6/24 | 7/28 | 8/32 | 9/36 | 10/40 | 11/44 | 12/48 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 | 18/24 | 21/28 | 24/32 | 27/36 | 30/40 | 33/44 | 36/48 |
| 1/5 | 2/10 | 3/15 | 4/20 | 5/25 | 6/30 | 7/35 | 8/40 | 9/45 | 10/50 | 11/55 | 12/60 |
| 2/5 | 4/10 | 6/15 | 8/20 | 10/25 | 12/30 | 14/35 | 16/40 | 18/45 | 20/50 | 22/55 | 24/60 |
| 3/5 | 6/10 | 9/15 | 12/20 | 15/25 | 18/30 | 21/35 | 24/40 | 27/45 | 30/50 | 33/55 | 36/60 |
| 4/5 | 8/10 | 12/15 | 16/20 | 20/25 | 24/30 | 28/35 | 32/40 | 36/45 | 40/50 | 44/55 | 48/60 |
| 1/6 | 2/12 | 3/18 | 4/24 | 5/30 | 6/36 | 7/42 | 8/48 | 9/54 | 10/60 | 11/66 | 12/72 |
| 5/6 | 10/12 | 15/18 | 20/24 | 25/30 | 30/36 | 35/42 | 40/48 | 45/54 | 50/60 | 55/66 | 60/72 |
| 1/7 | 2/14 | 3/21 | 4/28 | 5/35 | 6/42 | 7/49 | 8/56 | 9/63 | 10/70 | 11/77 | 12/84 |
| 2/7 | 4/14 | 6/21 | 8/28 | 10/35 | 12/42 | 14/49 | 16/56 | 18/63 | 20/70 | 22/77 | 24/84 |
| 3/7 | 6/14 | 9/21 | 12/28 | 15/35 | 18/42 | 21/49 | 24/56 | 27/63 | 30/70 | 33/77 | 36/84 |
| 4/7 | 8/14 | 12/21 | 16/28 | 20/35 | 24/42 | 28/49 | 32/56 | 36/63 | 40/70 | 44/77 | 48/84 |
| 5/7 | 10/14 | 15/21 | 20/28 | 25/35 | 30/42 | 35/49 | 40/56 | 45/63 | 50/70 | 55/77 | 60/84 |
| 6/7 | 12/14 | 18/21 | 24/28 | 30/35 | 36/42 | 42/49 | 48/56 | 54/63 | 60/70 | 66/77 | 72/84 |
| 1/8 | 2/16 | 3/24 | 4/32 | 5/40 | 6/48 | 7/56 | 8/64 | 9/72 | 10/80 | 11/88 | 12/96 |
| 3/8 | 6/16 | 9/24 | 12/32 | 15/40 | 18/48 | 21/56 | 24/64 | 27/72 | 30/80 | 33/88 | 36/96 |
| 5/8 | 10/16 | 15/24 | 20/32 | 25/40 | 30/48 | 35/56 | 40/64 | 45/72 | 50/80 | 55/88 | 60/96 |
| 7/8 | 14/16 | 21/24 | 28/32 | 35/40 | 42/48 | 49/56 | 56/64 | 63/72 | 70/80 | 77/88 | 84/96 |
| 1/9 | 2/18 | 3/27 | 4/36 | 5/45 | 6/54 | 7/63 | 8/72 | 9/81 | 10/90 | 11/99 | 12/108 |
| 2/9 | 4/18 | 6/27 | 8/36 | 10/45 | 12/54 | 14/63 | 16/72 | 18/81 | 20/90 | 22/99 | 24/108 |
| 4/9 | 8/18 | 12/27 | 16/36 | 20/45 | 24/54 | 28/63 | 32/72 | 36/81 | 40/90 | 44/99 | 48/108 |
| 5/9 | 10/18 | 15/27 | 20/36 | 25/45 | 30/54 | 35/63 | 40/72 | 45/81 | 50/90 | 55/99 | 60/108 |
| 7/9 | 14/18 | 21/27 | 28/36 | 35/45 | 42/54 | 49/63 | 56/72 | 63/81 | 70/90 | 77/99 | 84/108 |
| 8/9 | 16/18 | 24/27 | 32/36 | 40/45 | 48/54 | 56/63 | 64/72 | 72/81 | 80/90 | 88/99 | 96/108 |
Let’s see some examples.
Example 1:Find the two equivalent fractions for each of the following fractions.
Solution:
Example 2: Find the equivalent fraction of 
Solution:
Let’s divide the numerator and the denominator by 8 to get the equivalent fraction.
Example 3: Check the fractions 
and 
are equal or not.
Solution:
Example 4: Find the equivalent fraction of 
whose denominator is 21.
Solution:
We have given that the denominator of the equivalent fraction is 21. Let the numerator is n, so the equivalent fraction will be 
.
Example 5: Find the equivalent fraction of 
whose numerator is 15.
Solution:
We have given that the numerator of the equivalent fraction is 15. Let the denominator is d, so the equivalent fraction will be 
.
