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Assertion (A): The ratio 6 : 8 is equal to the ratio 3 : 4. Reason (R): Both parts of a ratio can be divided by the same number to get an equivalent ratio. Which is correct?

Class 6Ratio and ProportionRatio and Proportion
  • ABoth A and R are true, and R correctly explains A
  • BBoth A and R are true, but R does not explain A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

6 : 8 = 3 : 4 by dividing both parts by 2 (A is true). Dividing both parts of a ratio by the same number gives an equivalent ratio (R is true), and this is exactly why A holds.
Answer: A) Both A and R are true, and R correctly explains A

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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