Question 4 of 23intermediate🔧 ApplyTrue / False3 marks

Circle the following statements of proportion that are true. (i) 4 : 7 :: 12 : 21 (ii) 8 : 3 :: 24 : 6 (iii) 7 : 12 :: 12 : 7 (iv) 21 : 6 :: 35 : 10 (v) 12 : 18 :: 28 : 12 (vi) 24 : 8 :: 9 : 3

(i)
Answer

True. 4×214 \times 21 = 84 and 7×127 \times 12 = 84. Since both products are equal, the ratios are proportional.

(ii)
Answer

False. 8×68 \times 6 = 48 and 3×243 \times 24 = 72. Since 48 ≠\neq 72, the ratios are not proportional.

(iii)
Answer

False. 7×77 \times 7 = 49 and 12×1212 \times 12 = 144. Since 49 ≠\neq 144, the ratios are not proportional.

(iv)
Answer

True. 21×1021 \times 10 = 210 and 6×356 \times 35 = 210. Since both products are equal, the ratios are proportional.

(v)
Answer

False. 12×1212 \times 12 = 144 and 18×2818 \times 28 = 504. Since 144 ≠\neq 504, the ratios are not proportional.

(vi)
Answer

True. 24×324 \times 3 = 72 and 8×98 \times 9 = 72. Since both products are equal, the ratios are proportional.

Explanation

(i) Cross multiplication: 4×214 \times 21 = 84 and 7×127 \times 12 = 84. Since ad = bc, the statement is true. (ii) Cross multiplication: 8×68 \times 6 = 48 and 3×243 \times 24 = 72. Since ad ≠\neq bc, the statement is false. (iii) Cross multiplication: 7×77 \times 7 = 49 and 12×1212 \times 12 = 144. Since ad ≠\neq bc, the statement is false. (iv) Cross multiplication: 21×1021 \times 10 = 210 and 6×356 \times 35 = 210. Since ad = bc, the statement is true. (v) Cross multiplication: 12×1212 \times 12 = 144 and 18×2818 \times 28 = 504. Since ad ≠\neq bc, the statement is false. (vi) Cross multiplication: 24×324 \times 3 = 72 and 8×98 \times 9 = 72. Since ad = bc, the statement is true. Also, both ratios simplify to 3:1.

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