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Maths Gcse Wjec-Eduqas Higher

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Exam code:C300

Working with ratios

How do I share an amount in a given ratio?

  • Add together all parts in the ratio to find the total number of parts in the whole

    • $200 is to be shared between two people, A and B, in the ratio 5:3

    • There are 8 “parts” in total, as A receives 5 parts and B receives 3 parts

  • Divide the amount being shared by the total number of parts

    • $200 must be split into 8 parts, so this means that 1 part must be worth $25

      • 200 ÷ 8 = 25

  • Multiply the amount each part is worth by the number of parts for each quantity in the ratio

    • Person A receives 5 parts, each worth $25

      • 5 × 25 = $125 for person A

    • Person B receives 3 parts, each worth $25

      • 3 × 25 = $75 for person B

  • Check the values in the new ratio add up to the total amount being shared 

    • $125 + $75 = $200

Examiner Tips and Tricks

  • Adding labels to your ratios will help make your working clearer and help you remember which number represents which quantity, e.g. table row straight A colon straight B row 3 colon 4 end table

Worked Example

A particular shade of pink paint is made using three parts red paint, to two parts white paint.
Mark needs 60 litres of pink paint in order to decorate a room in his house.

Calculate the volume of red and white paint that Mark needs to purchase in order to have enough paint to decorate the room.

The ratio of red to white is

3 : 2

Adding these together gives the total number of parts

3 + 2 = 5

The total amount of paint is 60 litres

∴ 5 parts = 60 litres

Divide both sides by 5 to find out the number of litres in one part

table row blank blank cell table row cell 5 space parts end cell equals cell 60 space litres end cell row cell divided by 5 end cell blank cell divided by 5 end cell row cell 1 space part end cell equals cell 12 space litres end cell end table end cell end table

The ratio was 3:2, so multiply both number of parts by 12

<img alt=”table row space straight R colon straight W space row space 3 colon 2 space row cell table row cell cross times 12 end cell downwards arrow end table end cell space space space cell table row downwards arrow cell cross times 12 end cell end table end cell row space 36 colon 24 space end table” data-mathml='<math ><semantics><mtable ><mtr><mtd><mo>&#160;</mo></mtd><mtd><mi mathvariant=”normal”>R</mi></mtd><mtd><mo>:</mo></mtd><mtd><mi mathvariant=”normal”>W</mi></mtd><mtd><mo>&#160;</mo></mtd></mtr><mtr><mtd><mo>&#160;</mo></mtd><mtd><mn>3</mn></mtd><mtd><mo>:</mo></mtd><mtd><mn>2</mn></mtd><mtd><mo>&#160;</mo></mtd></mtr><mtr><mtd><mtable><mtr><mtd><mo>&#215;</mo><mn>12</mn></mtd><mtd><mo>&#8595;</mo></mtd></mtr></mtable></mtd><mtd><mo>&#160;</mo></mtd><mtd><mo>&#160;</mo></mtd><mtd><mo>&#160;</mo></mtd><mtd><mtable><mtr><mtd><mo>&#8595;</mo></mtd><mtd><mo>&#215;</mo><mn>12</mn></mtd></mtr></mtable></mtd></mtr><mtr><mtd><mo>&#160;</mo></mtd><mtd><mn>36</mn></mtd><mtd><mo>:</mo></mtd><mtd><mn>24</mn></mtd><mtd><mo>&#160;</mo></mtd></mtr></mtable><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”working” height=”112″ role=”math” 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