Question

A plumber needs to drill a hole that is just slightly larger than 3/16 in in diameter. Which measure is the smallest but still larger than 3/16 in? 5/32 in 5/16 and 13/64 in or 9/32 in

Answer 1

`(13)/(64)\ in` is the smallest but still larger than
`(3)/(16)\ in`

Explanation:

Given:

Plumber needs to drill a hole slightly larger than
`(3)/(16)\ in` in diameter.

The fractions of lengths to compare are :
`(5)/(32)\ in,(5)/(16)\ in, (13)/(64)\ in, (9)/(32)\ in`

Solution:

Comparing all fractions by taking LCD.

`(3)/(16)\ in,(5)/(32)\ in,(5)/(16)\ in, (13)/(64)\ in, (9)/(32)\ in`

Taking LCD = 64 and multiplying numerator and denominator of each fraction to make the denominators common.

`(3* 4)/(16* 4)\ in,(5* 2)/(32* 2)\ in,(5* 4)/(16* 4)\ in, (13)/(64)\ in, (9* 2)/(32* 2)\ in`

`(12)/(64)\ in,(10)/(64)\ in,(20)/(64)\ in, (13)/(64)\ in, (18)/(64)\ in`

Arranging the fractions in ascending order by comparing the numerators.

`(10)/(64)\ in< (12)/(64)\ in<(13)/(64)\ in<(18)/(64)\ in<(20)/(64)\ in`

This can be arranged in the original form as:

`(5)/(32)\ in<(3)/(16)\ in<(13)/(64)\ in< (9)/(32)\ in< (5)/(16)\ in`

Thus, we find out that
`(13)/(64)\ in` is the smallest but still larger than
`(3)/(16)\ in`