Adding & Subtracting Fractions

(a) Find $\frac{2}{3} + \frac{1}{5}$

Find the lowest common denominator of 3 and 5

15 is the smallest number that divides both 3 and 5

the lowest common denominator is 15

Write both fractions as equivalent fractions over 15 (by multiplying top and bottom by the same amount)

$\frac{2 \times 5}{3 \times 5} + \frac{1 \times 3}{5 \times 3} = \frac{10}{15} + \frac{3}{15}$

Add the numerators and write over a single denominator

$\frac{10 + 3}{15} = \frac{13}{15}$

There is no cancellation

$\frac{13}{15}$

(b) Find $3 \frac{3}{4} - \frac{5}{8}$ giving your answer as a mixed number

Change the mixed number into a top heavy fraction (by multiplying the denominator, 4, by the whole number, 3, then adding the numerator, 3)

$\frac{4 \times 3 + 3}{4} = \frac{15}{4}$

To find $\frac{15}{4} - \frac{5}{8}$ first find the lowest common denominator of 4 and 8

8 is the smallest number that divides both 4 and 8

the lowest common denominator is 8

Write both fractions as equivalent fractions over 8 (by multiplying top and bottom by the same amount)

$\frac{15 \times 2}{4 \times 2} - \frac{5 \times 1}{8 \times 1} = \frac{30}{8} - \frac{5}{8}$

Subtract the numerators and write over a single denominator

$\frac{30 - 5}{8} = \frac{25}{8}$

Change into a mixed number (by dividing 25 by 8 to get 3 remainder 1)

$= 3 \frac{1}{8}$

There is no more cancellation

$3 \frac{1}{8}$

Adding & Subtracting Fractions (CIE IGCSE Maths: Core)