Ratios-With-Fractions-Decimals-And-Percentages Wjec-Eduqas Foundation

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Exam code:C300

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 $5 over 8$ of the pizza
  - The second person receives $3 over 8$ 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 $3 over 40$ of the people in the school who are members of staff, $2 over 3$ of them wore Christmas jumpers on a particular day
  - That means $3 over 40 space cross times space 2 over 3 space equals space 6 over 120 space equals space 1 over 20$ 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 $37 over 40$ 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
  - $37 over 40 space cross times space 0.88 space equals space 0.814$ , 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

Examiner Tips and Tricks

In these types of questions it is really important to read the question carefully, so that you are clear about which bits are referring to what!
Give your final answer in the form asked for by the question (fraction, ratio, or percentage).

Worked Example

A shop sells only two flavours of crisps – Stilton Surprise and Pickled Haggis. Packages of those two flavours of crisps only occur in two sizes – regular and jumbo.

The ratio of packages of Stilton Surprise crisps to packages of Pickled Haggis crisps in the shop is 7:3.

30% of the packages of Stilton Surprise crisps are regular sized.
$2 over 5$ of the packages of Pickled Haggis crisps are regular sized.

What percentage of all the packages of crisps in the shop are jumbo sized?

Method 1 (Pure fractions and p

Maths Gcse Wjec-Eduqas Foundation