Option A
Answer:
[tex]\frac{36}{54} \text { and } \frac{6}{9}[/tex] are proportional.
Solution:
If two fractions are equal, than it is said to be in proportion.
Case 1:
Consider option A
Given fractions are [tex]\frac{36}{54} \text { and } \frac{6}{9}[/tex]
[tex]\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}[/tex]
Hence both the fractions are equal. So they are propotional.
Case 2:
Consider option 2
Given fractions [tex]\frac{6}{7} \text { and } \frac{16}{21}[/tex] cannot be simplified further. Also both the fractions are not equal. So they are not propotional.
Case 3:
Consider option 3
Given fractions are [tex]\frac{21}{36} \text { and } \frac{21}{42}[/tex]
[tex]\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}[/tex]
Hence [tex]\frac{7}{12} \text { and } \frac{1}{2}[/tex] are not equal. Hence they are not propotional.
Case 4:
Consider option 4
Given fractions are [tex]\frac{14}{35} \text { and } \frac{21}{42}[/tex]
[tex]\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}[/tex]
Hence [tex]\frac{2}{5} \text { and } \frac{1}{2}[/tex] are not equal. Hence they are not propotional.
The answer for the given question is option A
