Adding & Subtracting Fractions (Cambridge (CIE) IGCSE Maths: Core): Revision Note

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

Answer:

Find the lowest common denominator of 3 and 5
15 is the smallest number that can be divided by both 3 and 5

The lowest common denominator is 15

Write both fractions as equivalent fractions with a common denominator of 15
Multiply the numerator and denominator of the first fraction by 5
Multiply the numerator and denominator of the second fraction by 3

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

Add the numerators and write over a single denominator

$\frac{10+3}{15}=\frac{13}{15}$ 

There are no common factors that will cancel

$\frac{13}{15}$

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

Answer:

Change the mixed number into an improper fraction

Multiply the denominator by the whole part and add to the numerator
Write this value over the denominator

$\frac{4\times 3+3}{4}=\frac{15}{4}$ 

Find the lowest common denominator of 4 and 8
8 is the smallest number that by divided by both 4 and 8
The lowest common denominator is 8

Write both fractions as equivalent fractions over 8
Multiply the numerator and denominator of the first fraction by 2

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

Subtract the numerators and write over a single denominator

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

Change into a mixed number
Divide 25 by 8 to get 3 remainder 1

$3\frac{1}{8}$