Question

Write each set of fractions with the lowest common denominator and then find which fraction is greater. 4/7 and 5/8 3/8 and 4/9 5/6 and 7/8 3/10 and 4/15

Answer 1

`(32)/(56)\ < (35)/(56)`

`(27)/(72) \ < (32)/(72)`

`(20)/(24)\ < (21)/(24)`

`(9)/(30)\ >(8)/(30)`

Explanation:

Given that,

First set of fraction is
`(4)/(7)\ and \ (5)/(8)`.

Second set of fraction is
`(3)/(8)\ and \ (4)/(9)`.

Third set of fraction is
`(5)/(6)\ and \ (7)/(8)`.

Fourth set of fraction is
`(3)/(10)\ and \ (4)/(15)`.

Now,

Considering the first set of fraction:

LCM of 7 and 8 is 56. Now, multiply by 8 to both numerator and denominator to
`(4)/(7)`. and multiply by 7 to both the numerator and denominator to
`(5)/(8)`. We get new set of fraction as
`(32)/(56)\ and\ (35)/(56)`.

∴
`(32)/(56)\ < (35)/(56)`

Again considering the second set of fraction:

LCM of 8 and 9 is 72. Now, multiply by 9 to both the numerator and denominator to
`(3)/(8)`. and multiply by 8 to both the numerator and denominator to
`(4)/(9)`. We get new set of fraction as
`(27)/(72) \ and \ (32)/(72)`.

∴
`(27)/(72) \ < (32)/(72)`.

Again considering the third set of fraction:

LCM of 6 and 8 is 24. Now, multiply by 4 to both the numerator and denominator to
`(5)/(6)`. and multiply by 3 to both the numerator and denominator to
`(7)/(8)`. We get the new set of fraction as
`(20)/(24)\ and \ (21)/(24)`.

∴
`(20)/(24)\ < (21)/(24)`.

Again considering the fourth set of fraction:

LCM of 10 and 15 is 30.Now, multiply by 3 to both the numerator and denominator to
`(3)/(10)`. and multiply by 2 to both the numerator and denominator to
`(4)/(15)`.We, get the new set of fraction as
`(9)/(30)\ and \ (8)/(30)`.

∴
`(9)/(30)\ >(8)/(30)`