In mathematics, identical fractions are simply fractions with various numerators and also denominators but represent the same proportion the a whole. Equivalent fractions seem come be different at a look, however 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 tantamount fractions have actually an same amount or value after simplification of both their numerator and denominators. The fractions will generate the same value if cancellation through a common factor is made on both the numerator and denominator.

What are indistinguishable Fractions?

Equivalent fractions space two or more fractions that result in the same value after ~ simplification. Expect a/b and c/d room two fractions, climate the fractions are equivalent only if the leveling 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 indistinguishable of 5/15 because of leveling of 5/15 results in the same value together 1/3.

Now the question arises for why this fractions room equal in spite of having various numbers. The answer come this questions is that the fractions contain numerators and also denominators that space not co-prime numbers. Because of this they have actually a usual multiple i m sorry on department produces the exact 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, however after dividing 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 presented that either separating the denominator or multiply the numerator with the same factor does not change the value of the fraction. And therefore, equivalent fractions have an equal value once simplified.

How do you discover equivalent fractions?

Consider a case with the fraction 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 have the right to be concluded that:

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

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

Example 1:

Given the the fountain 5/16 and x/12 are indistinguishable calculate the value 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 value of x if the fountain 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 up to 5 tantamount fractions for each that the following:

(i) 3/4

(ii) 4/5

(iii) 6/7

(iv) 4/5

2. Find the tantamount fractions having actually a denominator of 12 for each the the adhering to fractions.

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(i) 1/2

(ii) 1/3

(iii) 3/4

(iv) 5/6

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

(ii) 3/8

(iii) 2/6

(iv) 4/6

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

(ii) 3/7 and 12/28

(iii) 5/8 and 15/27

(iv) 36/44 and 9/11

(v) 4/5 and 5/4

(vi) 5/8 and also 27/18

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

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

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

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

9. John carried out a survey in his class and also discovered that 56/96 the the students sampled out participated in sporting activities after school. Refer the fraction in its most basic form?

10. 7 is a prime number in a fraction 7/x. What number have the right to replace x in this fraction so that it is no in most basic form?