Question

What fraction lies exactly halfway between
1/2 and 2/3

Answer 1

`(7)/(12)`

Explanation:

Method 1

convert the fractions so that their denominators are 12:

`\frac12=(1 * 6)/(2 * 6)=(6)/(12)`

`\frac23=(2*4)/(3*4)=(8)/(12)`

From inspection, we can determine that the fraction that lies exactly halfway between
`(6)/(12)` and
`(8)/(12)` is
`(7)/(12)`

Method 2

Find the difference between the fractions and divide by 2:

`(\frac23-\frac12)/(2)=(1)/(12)`

Add this to the smallest fraction (1/2):

`\frac12+(1)/(12)=(7)/(12)`