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Rehan tested whether 5, 9, 15 and 27 are in proportion by adding: 5 + 27 = 32 and 9 + 15 = 24. Since the sums differ he decided they are not in proportion. Is he right?

Class 6Ratio and ProportionRatio and Proportion
  • AYes — the two sums are unequal, so the numbers are not in proportion
  • BNo — the correct test is the cross product, and , so they ARE in proportion
  • CYes — 5, 9, 15 and 27 share no common factor
  • DNo — he should have added the two middle terms only

Step-by-Step Solution

Proportion is about multiplication, not addition. For 5 : 9 :: 15 : 27 the extremes give and the means give . The products are equal, so the numbers ARE in proportion — Rehan's addition test led him to the wrong conclusion.
Answer: B) No — the correct test is the cross product, and , so they ARE in proportion

Key idea: Proportion: when two ratios are equal

If a : , the four numbers are in proportion. The classic check: the **product of the extremes** equals the **product of the means** . Example: are 4 : 6 and 6 : 9 in proportion? Cross-multiply: . Equal → yes, in proportion.

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