Question

Which pair of fractions are proportional? A)36/54 and 6/9 B)6/7and 16/21 C) 21/36and 21/42 D) 14/35 and 21/42

Answer 1

The answer is A. 36/54 and 6/9.

Answer 2

Option A

Answer:  

$\frac{36}{54} \text { and } \frac{6}{9}$ are proportional.

Solution:

If two fractions are equal, than it is said to be in proportion.

Case 1:  

Consider option A

Given fractions are $\frac{36}{54} \text { and } \frac{6}{9}$

$\frac{36}{54}=\frac{9 \times 2 \times 2}{9 \times 2 \times 3}=\frac{2}{3} \text { and } \frac{6}{9}=\frac{2 \times 3}{3 \times 3}=\frac{2}{3}$

Hence both the fractions are equal. So they are propotional.

Case 2:

Consider option 2

Given fractions $\frac{6}{7} \text { and } \frac{16}{21}$ cannot be simplified further. Also both the fractions are not equal. So they are not propotional.

Case 3:

Consider option 3

Given fractions are $\frac{21}{36} \text { and } \frac{21}{42}$

$\frac{21}{36}=\frac{7 \times 3}{6 \times 6}=\frac{7}{12} \text { and } \frac{21}{42}=\frac{7 \times 3}{6 \times 7}=\frac{1}{2}$

Hence $\frac{7}{12} \text { and } \frac{1}{2}$ are not equal. Hence they are not propotional.

Case 4:

Consider option 4  

Given fractions are $\frac{14}{35} \text { and } \frac{21}{42}$

$\frac{14}{35}=\frac{7 \times 2}{7 \times 5}=\frac{2}{5} \text { and } \frac{21}{42}=\frac{7 \times 3}{7 \times 6}=\frac{1}{2}$

Hence $\frac{2}{5} \text { and } \frac{1}{2}$ are not equal. Hence they are not propotional.

The answer for the given question is option A