Sharing an Amount in a Ratio (SQA National 5 Applications of Mathematics): Revision Note

Sharing an amount in a ratio

How do I share an amount in a given ratio?

• STEP 1
  Add together all parts in the ratio to find the total number of parts

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

  • There are 8 parts in total

    • A receives 5 parts and B receives 3 parts

• STEP 2
  Divide the amount being shared by the total number of parts

  • £200 must be split into 8 parts

    • 1 part equals £200 ÷ 8 = £25

• STEP 3
  Multiply the amount each part is worth by the number of parts for each quantity in the ratio

  • Person A receives 5 parts

    • 5 × 25 = £125 for person A

  • Person B receives 3 parts

    • 3 × 25 = £75 for person B

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

    • £125 + £75 = £200

How do I find quantities in a ratio if I don't know the total amount?

• STEP 1
  Identify the number of parts that correspond to the given quantity

  • Consider two people (A and B) sharing money in the ratio 5 : 3

    • If person A receives £90 then £90 is equal to 5 parts

    • If person B receives £90 then £90 is equal to 3 parts

    • If person A receives £90 more than person B then £90 is equal to 5 - 3 = 2 parts

• STEP 2
  Divide the quantity by the number of parts to find the value of one part

  • If person A receives £90 then 1 part is equal to £90 ÷ 5 = £18

  • If person B receives £90 then 1 part is equal to £90 ÷ 3 = £30

  • If person A receives £90 more than person B then 1 part is equal to £90 ÷ 2 = £45

• STEP 3
  Multiply this by the number of parts in each of the unknown quantities

  • If person A receives £90 then B receives 3 × £18 = £54

  • If person B receives £90 then A receives 5 × £30 = £150

  • If person A receives £90 more than person B then

    • A receives 5 × £45 = £225

    • B receives 3 × £45 = £135

    • the total received is (5 + 3) × £45 = £360