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

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For example, the equivalent fractions because that 1/4 are:

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

The indistinguishable fractions have actually an equal amount or value after simplification of both their numerator and denominators. The fractions will certainly generate the exact same value if cancellation by a common factor is make on both the numerator and denominator.

What are identical Fractions?

Equivalent fractions room two or more fractions that an outcome in the very same value after ~ simplification. Intend a/b and c/d are two fractions, climate the fountain are equivalent only if the simplification of each portion results in e/f.

In various other words,

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

For example, a fraction 1/3 has an identical of 5/15 since of simplification of 5/15 results in the same value together 1/3.

Now the concern arises because that why this fractions space equal despite having various numbers. The answer come this query is that the fountain contain numerators and also denominators that room not co-prime numbers. Therefore they have actually a common multiple which on department produces the very same value.

Let’s take an example:

1/2 = 2/4 = 4/8

You can notice that however the above two factions have different integers, but after dividing both the numerator and also denominator by a common factor, the an outcome is:

(4 ÷ 4)/(8 ÷ 4)

=1/2

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

(2 ÷ 2)/(4 ÷ 2)

= 1/2

It has been shown that either separating the denominator or multiply the numerator with the same aspect does not transform the worth of the fraction. And therefore, indistinguishable fractions have an same value as soon as simplified.

How do you find equivalent fractions?

Consider a situation with the portion 1/5.

Multiplying both the numerator and denominator v 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 concluded that:

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

The equivalent portion can only be produced by multiplication or department by a common factor. Carrying out addition or individually on the fraction only transforms the value of a fraction.

Example 1:

Given that the fountain 5/16 and also x/12 are tantamount 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 worth of x is 15/4.

Example 2:

Find the worth of x if the fountain 3/5 and also 4/x are equivalent.

Solution

Given that,

3/5 = 4/x

x = (4 x 5)/3

x = 20/3

Practice Questions

1. Write up to 5 equivalent fractions because that each of the following:

(i) 3/4

(ii) 4/5

(iii) 6/7

(iv) 4/5

2. Uncover the indistinguishable fractions having a denominator that 12 because that each the the complying with fractions.

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(i) 1/2

(ii) 1/3

(iii) 3/4

(iv) 5/6

3. Adjust the adhering to fractions into identical fractions having actually a value of 24 together their denominator:(i) 6/12

(ii) 3/8

(iii) 2/6

(iv) 4/6

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

(ii) 3/7 and 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 an equivalent fraction to 10/15 through 2 as the numerator. What fraction with a molecule of 2 am I thinking of?

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

7. James is offering his brother 2/5 of her nut collection. Calculate how numerous of 1/5 s that his nut repertoire is he giving his brother?

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

9. John performed a inspection in his class and discovered that 56/96 the the students sampled the end participated in sports after school. Express the fraction in its simplest form?

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