In mathematics, identical fractions are merely fractions with various numerators and denominators but represent the same proportion of a whole. Indistinguishable fractions seem come be various at a look, yet they have similar or equal value.

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

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

The equivalent 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 by a typical factor is made on both the numerator and also denominator.

What are equivalent Fractions?

Equivalent fractions space two or more fractions that result in the same value ~ simplification. Mean a/b and c/d are two fractions, then the fractions 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 portion 1/3 has an tantamount of 5/15 since of leveling of 5/15 results in the exact same value as 1/3.

Now the question arises because that why these fractions space equal regardless of having various numbers. The answer to this query is that the fractions contain numerators and also denominators that space not co-prime numbers. Thus they have a common multiple i beg your pardon on division produces the same value.

Let’s take it an example:

1/2 = 2/4 = 4/8

You can an alert that yet the above two factions have various integers, but after dividing both the numerator and also denominator through a typical factor, the an outcome is:

(4 ÷ 4)/(8 ÷ 4)

=1/2

In this case, if we leveling 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 multiplying the numerator with the same variable does not alter the worth of the fraction. And also therefore, indistinguishable fractions have an same value when simplified.

How carry out you find equivalent fractions?

Consider a situation with the fraction 1/5.

Multiplying both the numerator and also denominator through 2, 3 and also 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 fraction can just be generated by multiplication or department by a usual factor. Transferring out addition or individually on the portion only changes the worth of a fraction.

Example 1:

Given the the fountain 5/16 and also x/12 are equivalent 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 fountain 3/5 and also 4/x room 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. Discover the indistinguishable fractions having actually a denominator of 12 because that each that 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 indistinguishable fractions having actually a value of 24 together their denominator:(i) 6/12

(ii) 3/8

(iii) 2/6

(iv) 4/6

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

(ii) 3/7 and 12/28

(iii) 5/8 and also 15/27

(iv) 36/44 and also 9/11

(v) 4/5 and also 5/4

(vi) 5/8 and also 27/18

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

6. Erick notices that 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 her nut collection. Calculation how countless of 1/5 s that his nut repertoire is he giving his brother?

8. Peter gave 1/4 and also 3/12 of orange to Donald and Pedro, respectively. Determine if he provided out one equivalent portion of an orange.

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

10. 7 is a prime number in a fraction 7/x. What number can replace x in this portion so that it is not in easiest form?