Question

How can I solve ¾ - (-5/12)?

Answer 1

`1 (1)/(6)`

Explanation:

`(3)/(4)+ (5)/(12) =?\\`

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

`((3)/(4)` ×
`(3)/(3) )` +
`((5)/(12)` ×
`(1)/(1))=?`

Complete the multiplication and the equation becomes

`(9)/(12) + (5)/(12)`

The two fractions now have like denominators so you can add the numerators.

`(9+5)/(12) = (14)/(12)`

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 14 and 12 using

GCF(14,12) = 2

14÷2 / 12÷2 =7/6

The fraction

7/6

is the same as

7÷6

Convert to a mixed number using

long division for 7 ÷ 6 = 1R1, so

7/6=
`1 (1)/(6)`

Therefore:

3/4 − (−5/12) =
`1 (1)/(6)`

Solution by Formulas

Apply the fractions formula for subtraction, to

3/4 − (−5/12)

and solve

(3×12) − (−5×4) 4×12

=3/6− (−20/48)

=56/48

Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF( 56,48) = 8

56÷8 / 48÷8 =7/6

Convert to a mixed number using

long division for 7 ÷ 6 = 1R1, so

7/6=
`1 (1)/(6)`

Therefore:

3/4 − (-5/12) =
`1 (1)/(6)`