In mathematics, tantamount fractions are simply fractions with various numerators and denominators however represent the same proportion that a whole. Identical fractions seem to be different at a look, but they have similar or equal value.

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For example, the tantamount fractions for 1/4 are:

2/8, 3/12, 4/16, etc.

The indistinguishable fractions have actually an same amount or value after simplification of both your numerator and also denominators. The fractions will generate the exact same value if cancellation through a common factor is do on both the numerator and also denominator.

## What are indistinguishable Fractions?

Equivalent fractions space two or an ext fractions that result in the very same value after simplification. Mean a/b and c/d room two fractions, climate the fountain are identical only if the leveling of each portion results in e/f.

In various other words,

a/b = c/d = e/f.

For example, a fraction 1/3 has actually an tantamount of 5/15 because of simplification of 5/15 results in the exact same value together 1/3.

Now the concern arises for why these fractions space equal despite having various numbers. The answer come this ask is the the fractions contain numerators and also denominators that are not co-prime numbers. Thus they have actually a common multiple i m sorry on division produces the same value.

Let’s take an example:

1/2 = 2/4 = 4/8

You can notification that however the over two factions have different integers, but after dividing both the numerator and also denominator through a common factor, the result is:

(4 ÷ 4)/(8 ÷ 4)

=1/2

In this case, if we leveling 2/4, the result 1/2 again.

(2 ÷ 2)/(4 ÷ 2)

= 1/2

It has actually been displayed that either splitting the denominator or multiplying the numerator through the same factor does not transform the worth of the fraction. And therefore, tantamount fractions have actually an equal value when simplified.

## How do you discover equivalent fractions?

Consider a case with the portion 1/5.

Multiplying both the numerator and denominator with 2, 3 and 4 gives:

1/5 x 2/2 = 2/10

1/5 x 3/3 = 3/15

1/5 x 4/4 = 4/20

Therefore, it deserve to be finish that:

1/5 = 2/10 = 3/15 = 4/20

The equivalent portion can just be produced by multiplication or department by a common factor. Transferring out addition or subtraction on the fraction only changes the value of a fraction.

Example 1:

Given that the fountain 5/16 and also x/12 are identical calculate the worth of x.

Solution

Given that:

5/16 = x/12

x = (5 x 12)/16

x = 60/16

x =15/4

And thus, the value of x is 15/4.

Example 2:

Find the value of x if the fractions 3/5 and also 4/x space equivalent.

Solution

Given that,

3/5 = 4/x

x = (4 x 5)/3

x = 20/3

## Practice Questions

1. Write approximately 5 indistinguishable fractions because that each of the following:

(i) 3/4

(ii) 4/5

(iii) 6/7

(iv) 4/5

2. Uncover the identical fractions having a denominator that 12 because that each the the adhering to fractions.

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(i) 1/2

(ii) 1/3

(iii) 3/4

(iv) 5/6

3. Adjust the following fractions into identical fractions having actually a worth of 24 as their denominator:(i) 6/12

(ii) 3/8

(iii) 2/6

(iv) 4/6

4. Identify the pairs of fractions that space equivalent and which space not:(i) 2/3 and 8/12

(ii) 3/7 and also 12/28

(iii) 5/8 and 15/27

(iv) 36/44 and also 9/11

(v) 4/5 and 5/4

(vi) 5/8 and 27/18

5. Ns think of one equivalent portion to 10/15 through 2 as the numerator. What fraction with a numerator of 2 am I reasoning of?

6. Erick notices the either 3/5 or 3/4 is equal to the portion 12/20. Which portion is same to 12/20?

7. James is offering his brother 2/5 of she nut collection. Calculation how plenty of of 1/5 s of his nut collection is he providing his brother?

8. Peter offered 1/4 and 3/12 that orange come Donald and also Pedro, respectively. Identify if he offered out an equivalent portion of one orange.

9. John conducted a survey in his class and discovered the 56/96 the the student sampled out participated in sports after school. Refer the portion in its easiest form?

10. 7 is a element number in a fraction 7/x. What number have the right to replace x in this portion so that it is not in simplest form?