Three Equivalent Fractions

Multiplying the numerator and denominator of a fraction by the same (non-zero) number, the results of the new fraction is said to be equivalent to the original fraction. The word equivalent means that the two fractions have the same value. That is, they retain the same integrity - the same balance or proportion. Here we are going to study about how to find the equivalent fraction and its example problems. (Source from Wikipedia).

For example:

`2/3` = (2*2 / 3*2) = `4/6`

Therefore equivalent fraction for `2/3` = `4/6`

Example problems for equivalent fraction:

Example: 1

Fine the three equivalent fractions for `3/4`

Solution:

We know that equivalent fraction means multiply and divide by the same number .first we have to multiply and divide by 2 we get

= (3*2) / (4*2)

Simplify the above equation we get

= `6/8`

Second equivalent fraction:

Now we have multiply and divide by 3

= (3*3) / (4*3)

Simplify the above equation we get

= `9/12`

Third equivalent fraction

Now we have to multiply and divide by 4

= (3*4) / (4*4)

Simplify the above equation we get

= `12/16`

Therefore the three equivalent fractions is `6/8` , `9/12` , `12/16`

Example: 2

Find the three equivalent fractions for `4/6`

Solution:

First equivalent fraction:

Multiply and divide by 2

= (4*2) / (6*2)

Simplify the above equation we get

= `8 /12`

Second equivalent fraction:

Multiply and divide by 3

= (4*3) / (6*3)

Simplify the above equation we get

= `12 / 18`

Third equivalent fraction

Multiply and divide by 5

= (4*5) / (6*5)

Simplify the above equation we get

= `20 / 30`

Therefore the three equivalent fractions are `8/12, 12/18, 20/30`

Example: 3

Find the three equivalent fractions for `6/7`

Solution:

First equivalent fraction:

Multiply and divide by 3

= (6*3) / (7*3)

Simplify the above equation we get

= `18 /21`

Second equivalent fraction:

Multiply and divide by 5

= (6*5) / (7*5)

=` 30 / 35`

Third equivalent fraction

Multiply and divide by 7

= (6*7) / (7*7)

Simplify the above equation we get

= 42 / 49

Therefore the three equivalent fractions are `18/21, 30/35, 42/49`

Algebra is widely used in day to day activities watch out for my forthcoming posts on T Distribution Confidence Interval and Advantages of Linear programming. I am sure they will be helpful.

Practice problem for eqivalent fractions:

1. Find the three equivalent fractions for `5/7`

Answer =` 10/14, 15/21, 20/28`

2. Fine the three equivalent fractions for` 3/5`

Answer =` 6/10, 12/20, 15/25`

3. Find the three equivalent fractions for `3/9`

Answer = `6/18 , 9/27,12/36`