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Ratios and Proportions

Learn how to share quantities in a given ratio and solve problems involving direct proportion.

Key Ideas

  • A ratio compares values, telling us how much of one thing there is compared to another.
  • The order of the numbers in a ratio matters.
  • To share a quantity in a ratio a:b, first find the total number of parts (a + b), then divide the total quantity by this number to find the value of one part.
  • Direct proportion means as one value increases, the other increases at the same rate.

Worked Examples

Example 1

Share $60 in the ratio 2:3.

Explanation

Total parts = 2 + 3 = 5 parts.

Value of one part = $60 ÷ 5 = $12.

First share = 2 parts × $12 = $24.

Second share = 3 parts × $12 = $36.

Check: $24 + $36 = $60.

Ready to Practice?

Test your understanding of Ratios and Proportions with targeted questions from our bank.

Common Mistakes
  • ×Dividing by one of the ratio numbers instead of the total number of parts.
  • ×Writing the answer in the wrong order.
Exam Tip

"Always check if your final answers add up to the original total amount."