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Express 900 m : 2 km in simplest form (1 km = 1000 m).

Class 6Ratio and ProportionRatio and Proportion
  • A450 : 1
  • B9 : 2
  • C20 : 9
  • D9 : 20

Step-by-Step Solution

2 km = 2000 m, so the ratio is 900 : 2000. The HCF of 900 and 2000 is 100, giving 9 : 20. Comparing 900 with 2 without converting gives 450 : 1, and simply dropping the zeros gives 9 : 2 — both ignore that metres and kilometres are different units.
Answer: D) 9 : 20

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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