Question

Write the pair of fractions as a pair of fractions with a common denominator of 3/4 and 5/8

Answer 1

The pair of fractions as a pair of fractions with a common denominator of 3/4 and 5/8 is
`(24)/(32) \text{ and } (20)/(32)`

Solution:

We have to write the given pair of fractions with a common denominator

Given fractions are:

`(3)/(4) \text{ and } (5)/(8)`

To make the denominator of both fractions common, we have to find L.C.M of denominators (Least common multiple )

Here the denominators are 4 and 8

L.C.M of 4 and 8

List all prime factors for each number.

Prime Factorization of 4 is: 2 x 2

Prime Factorization of 8 is: 2 x 2 x 2

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 = 8

Thus L.C.M of 4 and 8 is 32

Given fraction is:

`(3)/(4) \text{ and } (5)/(8)`

Multiply the denominator by a number so that it becomes 32 and multiply that same number with numerator also

`(3)/(4) = (3 * 8)/(4 * 8) = (24)/(32)`

`(5)/(8) = (5 * 4)/(8 * 4) = (20)/(32)`

Thus the pair of fractions as a pair of fractions with a common denominator of 3/4 and 5/8 is
`(24)/(32) \text{ and } (20)/(32)`