Question

Write whether each pair of ratios forms a portion.

(1) 12/7 and 36/21

Answer 1

The pair of ratios 12/7 and 36/21 form a proportion. Since the cross-products are equal, the pair of ratios forms a proportion.

Step-by-step explanation:

The pair of ratios 12/7 and 36/21 form a proportion.

To check if two ratios form a proportion, we set the cross-products equal to each other. In this case, we have:

12/7 = 36/21

By multiplying the numerator of the first ratio by the denominator of the second ratio and the numerator of the second ratio by the denominator of the first ratio, we get:

12 × 21 = 7 × 36

Which simplifies to:

252 = 252

Since the cross-products are equal, the pair of ratios forms a proportion.

Answer 2

Both ratios simplify to the same numbers, they form a proportion.

To determine whether each pair of ratios forms a proportion, they have to express the same relationship between numbers.

When the ratios are equivalent after simplification, they form a proportion. Let's evaluate the given ratios:

For the pair 12/7 and 36/21, simplify the second ratio by dividing both numerator and denominator by the same number, 3 in this case:

36 ÷ 3 = 12

21 ÷ 3 = 7

So, 36/21 simplifies to 12/7. Since both ratios simplify to the same numbers, they form a proportion.