Adding & Subtracting Fractions (Edexcel IGCSE Maths)

Spec point — 1.2F

Adding & subtracting fractions

How do I add or subtract two fractions?

• Addition and subtraction are treated in exactly the same way when dealing with fractions

  • Find the lowest common denominator

  • Write each fraction as an equivalent fraction over this denominator

  • Add (or subtract) the numerators and write this over a single denominator

    • Do not add the denominators

  • Simplify the fraction by cancelling common factors

What do I do if any of the fractions are mixed numbers?

• Convert any mixed numbers into improper fractions

  • Add or subtract the fractions as usual
  • Remember to convert the answer back to a mixed number if required

Exam Hint 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.

Worked Example (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

$\frac{2\times5}{3\times5}+\frac{1\times3}{5\times3}=\frac{10}{15}+\frac{3}{15}$* *

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

$\frac{4\times3+3}{4}=\frac{15}{4}$* *

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

$\frac{15\times2}{4\times2}-\frac{5}{8}=\frac{30}{8}-\frac{5}{8}$

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

$3\frac{1}{8}$