Basic Fractions (Cambridge International IGCSE Mathematics)

Basic fractions

What is a fraction?

• A fraction is written as $\frac{a}{b}$ where a and b are integers

  • The number on the top, a, is called the numerator
  • The number on the bottom, b, is called the denominator

• The values of the numerator and denominator tell us about the size of the fraction

  • The denominator is how many parts each whole number is split into

  • The numerator is how many parts you have

    • For example, $\frac{2}{3}$ means that each whole number is divided into 3 parts and you have 2 of these parts

• A fraction is less than 1 if the numerator is smaller than the denominator

• A fraction is more than 1 if the numerator is bigger than the denominator

How do I find a fraction of an amount?

• Method 1 Divide by the denominator and multiply by the numerator

  • To find $\frac{2}{5}$ of $60$, divide it by 5 then multiply it by 2

    • $60\div5=12$, then $12\times2=24$

• Method 2 Change the fraction into a decimal, then multiply

  • To find $\frac{9}{10}$ of $15$, turn $\frac{9}{10}$ into $0.9$ then multiply

    • $0.9\times15=13.5$

• Method 3 Write both numbers as fractions and multiply the two fractions together

  • To find $\frac{5}{6}$ of $8$, turn $8$ into $\frac{8}{1}$

    • Work out $\frac{5}{6}\times\frac{8}{1}=\frac{40}{6}=\frac{20}{3}$

What are equivalent fractions?

• Equivalent fractions are two fractions that represent the same amount

  • They are different ways of writing the same thing
  • For example, $\frac{1}{2}$ and $\frac{6}{12}$ are equivalent fractions

How do I find an equivalent fraction?

• To find an equivalent fraction, multiply the top and bottom of a fraction by the same number

  • $\frac{5}{6}$ is equivalent to $\frac{5\times2}{6\times2}=\frac{10}{12}$ and $\frac{5\times3}{6\times3}=\frac{15}{18}$ and $\frac{5\times4}{6\times4}=\frac{20}{24}$etc.
  • For each fraction, there are an infinite number of equivalent fractions

What is a simplified fraction?

• A simplified fraction is a fraction that is written using the smallest possible integer values

  • Simplifying turns a fraction into an 'easier' equivalent fraction

• If both the numerator and denominator can be divided by the same number (called a common factor), the fraction can be simplified

• Simplifying is also called cancelling a fraction

How do I simplify fractions?

• To simplify the fraction,divide the top and bottom by the common factor

• $\frac{12}{18}=\frac{12\div6}{18\div6}=\frac{2}{3}$

• $\frac{25}{45}=\frac{25\div5}{45\div5}=\frac{5}{9}$

Exam Hint Make use of your calculator in your exam:

• Typing any fraction into it and pressing equals will automatically simplify the fraction for you.
• If the question asks you to show your working, you must show which number you divided by.