Adding & Subtracting Fractions (Cambridge International IGCSE Mathematics)

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

Worked Example (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

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

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) 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

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

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

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

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

$3\frac{1}{8}$