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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, Equivalent Fractions is equal to Equivalent Fractions. Hence, Equivalent Fractions is an equivalent fraction of Equivalent Fractions. Similarly, Equivalent Fractions is also an equivalent fraction of Equivalent Fractions.

Equivalent Fractions

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 Equivalent Fractions are:

Equivalent Fractions

In the fraction Equivalent Fractions, we have multiplied the numerator and the denominator by 3 to get the equivalent fraction.

Equivalent Fractions

In the fraction Equivalent Fractions, we have multiplied the numerator and the denominator by 6 to get the equivalent fraction. Similarly, we can find more equivalent fractions of Equivalent Fractions.

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 Equivalent Fractions are:

Equivalent Fractions

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.

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.

Equivalent Fractions

Solution:

Equivalent Fractions

Example 2: Find the equivalent fraction of Equivalent Fractions

Solution:

Let's divide the numerator and the denominator by 8 to get the equivalent fraction.

Equivalent Fractions
Equivalent Fractions

Example 3: Check the fractions Equivalent Fractions and Equivalent Fractions are equal or not.

Solution:

Equivalent Fractions

Example 4: Find the equivalent fraction of Equivalent Fractions 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 Equivalent Fractions.

Equivalent Fractions

Example 5: Find the equivalent fraction of Equivalent Fractions 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 Equivalent Fractions.

Equivalent Fractions
Next TopicSimplify Fractions




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