Adding & Subtracting Fractions (Edexcel IGCSE Maths B): Revision Note

In most questions, you can just use your calculator to add or subtract fractions. However, sometimes you get asked to show your working without using a calculator. If you do not show your method, you get zero marks. The question is testing your ability to add or subtract fractions, not your calculator skills.

(a) Show that $\frac{2}{3}+\frac{1}{5}=\frac{13}{15}$.

Answer:

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) Show that $3\frac{3}{4}-\frac{5}{8}=3\frac{1}{8}$.

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

$\frac{4\times 3+3}{4}=\frac{15}{4}$ 

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

$3\frac{1}{8}$