Question

The fractions (7)/(12),x,(2)/(3) are written in increasing order of size. The fraction x is exactly halfway between (7)/(12) and (2)/(3) Find x in its simplest form.

Answer 1

(5/8)

Explanation:

(7/12), x, (2/3)

x is (1/2) the way between the other two fractions.

The difference in the outer two fractions is:

(2/3) - (7/12) = (8/12) - (7/12) [Multiply the first fraction by (4/4) to make its denominator the same as the second fraction (7/12)]

(2/3) - (7/12) = (1/12)

Half of (1/12): (1/12)*(1/2) = (1/24)

Fraction x must be (7/12) + (1/24)

(7/12) + (1/24)

(14/24) + (1/24) = (15/24)

(15/24) can be simplified to (5/8)