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Express 40 seconds : 3 minutes in simplest form (1 minute = 60 seconds).

Class 6Ratio and ProportionRatio and Proportion
  • A2 : 9
  • B9 : 2
  • C40 : 3
  • D4 : 18

Step-by-Step Solution

3 minutes = 180 seconds. Ratio = 40 : 180, and the HCF is 20, so 40÷20 : 180÷20 = 2 : 9. Leaving the answer as 40 : 3 compares seconds with minutes, and 4 : 18 has been divided by only 10, so it is not yet simplest.
Answer: A) 2 : 9

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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