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Using Fractions

Maths: Edexcel IGCSE Higher, topic 1.2.2

Adding and Subtracting Fractions

When we add or subtract fractions, we must make sure the denominator of both fractions is the same.

Same denominator

Same denominator

  • If the denominator of both fractions is already the same we simply add or subtract the numerators.
Same denominator 2

Same denominator 2

  • If the denominator of both fractions is already the same we simply add or subtract the numerators.
Different denominators

Different denominators

  • If the denominators are not the same we need to make them the same using an equivalent fraction.
Different denominators 2

Different denominators 2

  • When finding an equivalent fraction we must multiply or divide both the top and bottom row by the same amount.
Different denominators 3

Different denominators 3

  • Once both the fractions have the same denominator we can add or subtract the numerators.
What is $$\frac{3}{4} - \frac{1}{5}$$?

What is 34−15\frac{3}{4} - \frac{1}{5}?

  • We cannot do the subtraction straight away because the fractions do not have the same denominator.
What is $$\frac{3}{4} - \frac{1}{5}$$?

What is 34−15\frac{3}{4} - \frac{1}{5}?

  • Using equivalent fractions, convert the fraction so that they have the same denominator.
What is $$\frac{3}{4} - \frac{1}{5}$$?

What is 34−15\frac{3}{4} - \frac{1}{5}?

  • Once both the fractions have the same denominator we can add or subtract the numerators.

Multiplying and Dividing Fractions

When we multiply or divide fractions, we do NOT have to make sure the denominator of both fractions is the same.

Multiplying fractions

Multiplying fractions

  • To multiply two fractions we multiply the two numerators and multiply the two denominators.
Multiplying fractions 2

Multiplying fractions 2

  • To multiply two fractions we multiply the two numerators and multiply the two denominators.
Dividing fractions

Dividing fractions

  • To divide one fraction by another, we first swap the numerator and denominator of the second fraction (the one we are dividing by).
Dividing fractions 2

Dividing fractions 2

  • Once we have swapped the numerator and denominator we multiply the two fractions together.
What is $$\frac{3}{4} ÷ \frac{4}{7}$$?

What is \frac{3}{4} ÷ \frac{4}{7}?

What is $$\frac{3}{4} ÷ \frac{4}{7}$$?

What is \frac{3}{4} ÷ \frac{4}{7}?

  • It is possible that when dividing fractions we end up with an improper fraction, such as 2116\frac{21}{16}.

Finding a Fraction of a Quantity

When finding a fraction of a quantity, we are effectively just multiplying fractions.

What is $$\frac{2}{5}$$ of 90?

What is 25\frac{2}{5} of 90?

  • 90 can be written as 901\frac{90}{1} to make the multiplication easier.
  • We multiply the two numerators and the two denominators.
What is $$\frac{1}{6}$$ of 72?

What is 16\frac{1}{6} of 72?

  • Remember to write the starting amount as a fraction.

Test yourself on Using Fractions

  • What is 710−15\frac{7}{10} - \frac{1}{5}?

  • What is 49+16\frac{4}{9} + \frac{1}{6}?

  • Which of the following additions or subtractions of fractions are correct?

  • What is \frac{5}{6} × \frac{4}{7}?

  • Which of the following multiplications are correct?

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