Answer:
Options B and C are correct choices.
Step-by-step explanation:
We have been given 4 pairs of ratios. We are asked to choose the pairs that form a proportion.
We know that two quantities are proportional if their ratios are same.
Let us check our each pair.
A. One sixth and four over twenty.
Express as fractions and equate:
[tex]\frac{1}{6}=\frac{4}{20}[/tex]
[tex]\frac{1}{6}=\frac{4\cdot 1}{4\cdot 5}\\\\\frac{1}{6}\neq \frac{1}{5}[/tex]
Since ratio is not same, therefore, this pair is not proportional.
B. Seven ninths and twenty eight over thirty six.
Express as fractions and equate:
[tex]\frac{7}{9}=\frac{28}{36}\\\\\frac{7}{9}=\frac{4\cdot 7}{4\cdot 9}\\\\\frac{7}{9}=\frac{7}{9}[/tex]
Since ratio is same, therefore, this pair is proportional.
C. Fourteen over eighteen and twenty one over twenty seven.
Express as fractions and equate:
[tex]\frac{14}{18}=\frac{21}{27}\\\\\frac{2\cdot 7}{2\cdot 9}=\frac{3\cdot 7}{3\cdot 9}\\\\\frac{7}{9}=\frac{7}{9}[/tex]
Since ratio is same, therefore, this pair is proportional.
C. Thirty over eighty and six over eighteen.
Express as fractions and equate:
[tex]\frac{30}{80}=\frac{6}{18}\\\\\frac{10\cdot 3}{10\cdot 8}=\frac{6\cdot 1}{6\cdot 3}\\\\\frac{3}{8}\neq \frac{1}{3}[/tex]
Since ratio is not same, therefore, this pair is not proportional.
