Introduction-To-Ratios Aqa Foundation

Introduction to ratio

What is a ratio?

• A ratio is a way of comparing one part of a whole to another

  • Ratios are used to compare one part to another part

    • How many parts that make the whole will depend on the question

What do ratios look like?

• Ratios involve two or three different numbers separated using a colon

  • E.g. 2 : 5, 3 : 1, 4 : 2 : 3 

• In all ratio questions, who or what is mentioned first in the question, will be associated with the first part of the ratio

  • E.g. The cake recipe with flour and butter in the ratio 2 : 1

    • ‘Flour’ is associated with ‘2’ and ‘butter’ is associated with ‘1’

• The numbers in a ratio tell us, for each quantity involved, its proportion of the whole 

  • In the ratio 4 : 3

    • The first quantity comprises 4 parts (of the whole)

    • The second quantity comprises 3 parts (of the whole)

    • In total, the whole is made up of 4 + 3 = 7 parts

  • In the ratio 2 : 5 : 3

    • The first quantity comprises 2 parts (of the whole)

    • The second quantity comprises 5 parts (of the whole)

    • The third quantity comprises 3 parts (of the whole)

    • In total, the whole is made up of 2 + 5 + 3 = 10 parts

How are ratios and fractions linked?

• Fractions and ratios are closely linked and are used to compare a part of a whole

  • A fraction compares a part to the whole

  • A ratio compares one part to another part

• For example, a pizza is sliced into 8 pieces, and shared between two people such that the first person receives 5 slices, and the second person receives 3 slices

  • As a fraction (of the whole)

    • The first person receives of the pizza

    • The second person receives  of the pizza

• The ratio of slices of the first person to the second person is 5 : 3

  • The 8 does not appear in the ratio but is obtained by adding the parts together (5 + 3 = 8)

• Unlike ratios, fractions can be converted/expressed as percentages or decimals