In mathematics, equivalent fractions are merely fractions with different numerators and also denominators however represent the exact same proportion the a whole. Indistinguishable fractions seem to be different at a look, but they have comparable or same 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 leveling of both their numerator and also denominators. The fractions will certainly generate the same value if cancellation through a usual factor is do on both the numerator and also denominator.

What are identical Fractions?

Equivalent fractions space two or much more fractions that result in the exact same value ~ simplification. Suppose a/b and also c/d space two fractions, then the fractions are equivalent only if the simplification of each fraction results in e/f.

In other words,

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

For example, a fraction 1/3 has actually an identical of 5/15 due to the fact that of simplification of 5/15 outcomes in the very same value together 1/3.

Now the concern arises for why these fractions space equal regardless of having various numbers. The answer to this questions is the the fountain contain numerators and denominators that space not co-prime numbers. Thus they have actually a usual multiple i m sorry on department produces the very same value.

Let’s take it an example:

1/2 = 2/4 = 4/8

You can notice that yet the over two factions have various integers, yet after separating both the numerator and also denominator by a usual factor, the result is:

(4 ÷ 4)/(8 ÷ 4)

=1/2

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

(2 ÷ 2)/(4 ÷ 2)

= 1/2

It has actually been shown that either separating the denominator or multiply the numerator through the same element does not alter the worth of the fraction. And also therefore, indistinguishable fractions have actually an same value as soon as simplified.

How perform you uncover equivalent fractions?

Consider a case with the portion 1/5.

Multiplying both the numerator and also denominator through 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 can be break up that:

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

The equivalent portion can only be created by multiplication or division by a typical factor. Transporting out enhancement or subtraction on the fraction only alters the value of a fraction.

Example 1:

Given the 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 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 equivalent fractions because that each the the following:

(i) 3/4

(ii) 4/5

(iii) 6/7

(iv) 4/5

2. Discover the identical fractions having a denominator of 12 for each of the complying with fractions.

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(i) 1/2

(ii) 1/3

(iii) 3/4

(iv) 5/6

3. Readjust the complying with fractions into identical fractions having a worth of 24 together their denominator:(i) 6/12

(ii) 3/8

(iii) 2/6

(iv) 4/6

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

(ii) 3/7 and 12/28

(iii) 5/8 and also 15/27

(iv) 36/44 and 9/11

(v) 4/5 and 5/4

(vi) 5/8 and 27/18

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

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

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

8. Peter offered 1/4 and 3/12 that orange to Donald and also Pedro, respectively. Recognize if he gave out one equivalent fraction of an orange.

9. John carried out a inspection in his class and discovered that 56/96 the the student sampled out participated in sporting activities after school. To express the fraction in its most basic form?

10. 7 is a prime number in a fraction 7/x. What number can replace x in this fraction so that it is no in simplest form?