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GCSEMathsEdexcelHigherRevision Notes3. Ratio, Proportion & Rates of ChangeProblem Solving with RatiosRatios with Fractions, Decimals & Percentages

Ratios with Fractions, Decimals & Percentages (Edexcel GCSE Maths)

Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Edexcel Maths: HigherEdexcel Maths: 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 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 percentages method)

First find the fractions of each type of crisp
The ratio divides the crisps into 7+3=10 parts
7 of those parts are Stilton Surprise, and 3 of them are Pickled Haggis

fraction numerator 7 space over denominator 7 plus 3 end fraction space equals space 7 over 10 space are space Stilton space Surprise fraction numerator 3 space over denominator 7 plus 3 end fraction space equals space 3 over 10 space are space Pickled space Haggis

30% of the Stilton Surprise are regular sized
So multiply 7/10 by 0.3 to find the percentage that are Stilton Surprise and regular sized

7 over 10 space cross times space 0.3 space equals space 7 over 10 space cross times space 3 over 10 space equals space 21 over 100 space 21 over 100 space equals space 0.21 So space 21 percent sign space are space regular space sized space Stilton space Surprise

2/5 of the Pickled Haggis are regular sized
So multiply 3/10 by 2/5 to find the percentage that are Pickled Haggis and regular sized

3 over 10 space cross times space 2 over 5 space equals space 6 over 50 6 over 50 space equals space 12 over 100 space equals space 0.12 So space 12 percent sign space are space regular space sized italic space Pickled space Haggis

Add those together to find the percentage that are regular sized

21 space plus space 12 space equals space 33 percent sign space regular space sized

And finally subtract 33% from 100% to find the percentage that are jumbo sized

100 space minus space 33 space equals space 67

67% are jumbo sized

Method 2 ('Pick a number' method)

Start by assuming (for example) that there are 100 packages of crisps in the shop
The ratio divides the crisps into 7+3=10 parts
So divide 100 by 10 to find how many packages are in 1 part

100 space divided by space 10 space equals space 10 space packages

7 of those parts are Stilton Surprise, and 3 of them are Pickled Haggis
So multiply 10 by 7 and by 3 to find out how many packages of each type there are

7 space cross times space 10 space equals space 70 space are space Stilton space Surprise 3 space cross times space 10 space equals space 30 space are space Pickled space Haggis

30% of the Stilton Surprise are regular sized
So multiply 70 by 0.3 to find how many are Stilton Surprise and regular sized

table row cell 70 space cross times space 0.3 space end cell equals cell space 70 space cross times space 3 over 10 space space end cell row blank equals cell space 210 over 10 end cell row blank blank blank row blank equals cell space 21 space space are space regular space sized space Stilton space Surprise end cell end table

2/5 of the Pickled Haggis are regular sized
So multiply 30 by 2/5 to find how many are Pickled Haggis and regular sized

table row cell 30 space cross times space 2 over 5 space end cell equals cell space 60 over 5 end cell row blank blank blank row blank equals cell 12 space space are space regular space sized italic space Pickled space Haggis end cell end table

Add those together to find how many in total are regular sized

21 space plus space 12 space equals space 33 space space are space regular space sized

Subtract 33 from 100 to find how many are jumbo sized

100 space minus space 33 space equals space 67 space space are space jumbo space sized

And finally turn that into a percentage out of 100

67 over 100 space equals space 0.67

67% are jumbo sized

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.