Question

Question 1 of 5 Multiple Choice Select all the pairs of ratios that form a proportion.

A. one sixth and four over twenty
B. seven ninths and twenty eight over thirty six
C. fourteen over eighteen and twenty one over twenty seven
D. thirty over eighty and six over eighteen

Answer 1

B & D I believe

Explanation:

Sorry if I'm wrong

Answer 2

Options B and C are correct choices.

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:

`(1)/(6)=(4)/(20)`

`(1)/(6)=(4\cdot 1)/(4\cdot 5)\\\\(1)/(6)\\eq (1)/(5)`

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:

`(7)/(9)=(28)/(36)\\\\(7)/(9)=(4\cdot 7)/(4\cdot 9)\\\\(7)/(9)=(7)/(9)`

Since ratio is same, therefore, this pair is proportional.

C. Fourteen over eighteen and twenty one over twenty seven.

Express as fractions and equate:

`(14)/(18)=(21)/(27)\\\\(2\cdot 7)/(2\cdot 9)=(3\cdot 7)/(3\cdot 9)\\\\(7)/(9)=(7)/(9)`

Since ratio is same, therefore, this pair is proportional.

C. Thirty over eighty and six over eighteen.

Express as fractions and equate:

`(30)/(80)=(6)/(18)\\\\(10\cdot 3)/(10\cdot 8)=(6\cdot 1)/(6\cdot 3)\\\\(3)/(8)\\eq (1)/(3)`

Since ratio is not same, therefore, this pair is not proportional.