Ratios-With-Fractions-Decimals-And-Percentages Aqa Foundation

Ratios & FDP

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

How do I answer questions involving ratios along with fractions and/or percentages?

• In harder ratio questions, the information you are given may also involve fractions and/or percentages

• Remember that you can use multiplication to find fractions or percentages of something

  • E.g. Finding a fraction of a fraction 

    • Of the of the people in the school who are members of staff, of them wore Christmas jumpers on a particular day

    • That means of the people in the school that day were members of staff wearing Christmas jumpers

  • E.g. Finding a percentage of a fraction

    • Of the of the people in the school who are students, 88% of them wore Christmas jumpers on that same day

    • To find 88% of something, you can multiply it by 0.88

    • , so this means 81.4% of the people in the school that day were students wearing Christmas jumpers

• An alternative method is to ‘pick a number‘ for the total number of things in the question 

  • E.g. Assume there are a 1000 people in the school (this is not necessarily the actual total) 

  • You can calculate the percentages or fractions using real numbers

  • Remember to turn your final answer back into the correct form