Which pair of ratios are equivalent? Select one: A. 3/5 and 2/4 B. 7/14 and 1/3 C. 9/12 and 3/6 D. 3/4 and 6/8
Answers
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Answer:
Writing the ratios as fractions, we have
3 : 4 = 34 and 9 : 16 = 916
Now, LCM of 4 and 16 = 16.
Making the denominator of each fraction = 16, we have
34 = 3 × 44 × 4 = 1216 and the other fraction = 916
Of 1216 and 916, clearly 1216>916.
Therefore, 34>916.
(ii) Writing the ratios as fractions, we have
15 : 16 = 1516 and 24 : 25 = 2425
Now, LCM of 16 and 25 = 400.
Making the denominator of each fraction = 400, we have
1516 = 15 × 2516 × 25= 375400 and the other fraction = 24 × 1625 × 16= 384400
Clearly, 384 > 375. So, 384400 > 375400.
Therefore, 2425>1516.
(iii) Writing the ratios as fractions, we have
4 : 7 = 47 and 5 : 8 = 58
Now, LCM of 7 and 8 = 56.
Making the denominator of each fraction = 56, we have
4× 87 × 8= 3256 and the other fraction = 5 × 78 × 7= 3556
Clearly, 36 > 32. So, 3556 > 3256.
Therefore, 58>47.
(iv) Writing the ratios as fractions, we have
9 : 20 = 920 and 8 : 13 = 813
Now, LCM of 20 and 13 = 260.
Making the denominator of each fraction = 260, we have
9× 1320 × 13= 117260 and the other fraction = 8 × 2013 × 20= 160260
Clearly, 160 > 117. So, 160260 > 117260.
Therefore, 813>920.
(v) Writing the ratios as fractions, we have
1 : 2 = 12 and 13 : 27 = 1327
Now, LCM of 2 and 27 = 54.
Making the denominator of each fraction = 54, we have
1× 272 × 27= 2754 and the other fraction = 13 × 227 × 2= 2654
Clearly, 27 > 26. So, 2754 > 2654.
Therefore, 12>1327.