Question

What is the fraction that is found halfway between 5/16 and 7/11 ?

Answer 1

`167/352`

Explanation:

To find the fraction found halfway between `5/16` and `7/11` is to find the average of the two fractions.

Recall that the average is found by adding a certain amount of numbers together and dividing it by the amount of numbers in the set.

In your case, we must add `5/16` and `7/11` together and divide it by `2`, since there are two fractions.

Step 1: Adding the Two Fractions Together

Thus,

`5/16+7/11`

In order to add the two fractions together, find the L.C.M. of the two denominators of the fractions. As a shortcut, multiply each fraction by the denominator of the other fraction in the numerator and denominator.

`=5/16(11/11)+7/11(16/16)`

Simplify.

`=55/176+112/176`

`=color(blue)(167/176)`

Step 2: Dividing the Sum by 2

`color(blue)(167/176)-:2`

Recall that dividing by `2` is the same as multiplying by the reciprocal of `2`. Thus,

`=167/176*1/2`

`=color(green)(|bar(ul(color(white)(a/a)color(black)(167/352)color(white)(a/a)|)))`