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Express the ratio 63 : 84 in its simplest form.

Class 6Ratio and ProportionRatio and Proportion
  • A9 : 12
  • B21 : 28
  • C4 : 3
  • D3 : 4

Step-by-Step Solution

HCF of 63 and 84 is 21. 63÷21 = 3 and 84÷21 = 4, so the simplest form is 3 : 4. Dividing by only 3 gives 21 : 28 and dividing by only 7 gives 9 : 12 — both are equivalent ratios but neither is in SIMPLEST form. 4 : 3 reverses the order.
Answer: D) 3 : 4

Key idea: Equivalent ratios and simplest form

Just like equivalent fractions: multiply or divide both parts of a ratio by the same non-zero number to get an equivalent ratio. 2 : 3 = 4 : 6 = 6 : 9 = 20 : 30. The **simplest form** is when the two parts share no common factor other than 1. So 20 : 30 simplifies (divide both by 10) to 2 : 3.

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