Question

Which fraction is greater than 1/2 and less than 3/4 ?
​

Answer 1

a.
`(2)/(3)`

Explanation:

The fraction,
`(2)/(3)` is greater than
`(1)/(2)` and less than
`(3)/(4)`.

How do we know this? See below how the fractions are compared together.

First, compare
`(2)/(3)` and
`(1)/(2)`.

Find a common denominator for both fractions:

Common denominator of 2 and 3 would be 6. Therefore, multiply as follows:

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

`(1 * 3)/(2 * 3) = (3)/(6)`.

Compare the numerators. Which one is greater?

Form the calculation above:

`(2)/(3) = (4)/(6)` has a numerator of 4.

.

`(1)/(2) = (3)/(6)` has a numerator of 3.

Since 4 is greater than 3, therefore, the fraction,
`(2)/(3)` is greater than
`(1)/(2)`.

✍️Compare
`(2)/(3)` and
`(3)/(4)`.

Find a common denominator for both fractions

`(2 * 4)/(3 * 4) = (8)/(12)` and

`(3 * 3)/(4 * 3) = (9)/(12)`

Comparing their numerator, 8 is less than 9, therefore:

`(2)/(3)` is less than
`(3)/(4)`.

✔️We can conclude that:

`(2)/(3)` is greater than
`(1)/(2)`, and less than
`(3)/(4)`.