Question

Which two ratios represent quantities that are proportional:

A. (9/10 and 10/9) ,
B. (56/64 and 36/48) ,
C. (5/7 and 7/14)
D. (21/28 and 12/16)

Answer 1

The two ratios that represent proportional quantities are (21/28 and 12/16). After simplifying both ratios, they are each equivalent to 3/4, making them proportional.

Step-by-step explanation:

We need to determine which two ratios represent quantities that are proportional. Proportions occur when two ratios are equivalent. To test if the given ratios represent proportions, we can cross-multiply and see if the products are equal.

1. (9/10 and 10/9): Cross-multiplication gives us 9*9 and 10*10 which are 81 and 100, respectively. These are not equal, so these are not proportional.
2. (56/64 and 36/48): Simplify both ratios to their lowest terms. (56/64) simplifies to 7/8 and (36/48) simplifies to 3/4. Since 7/8 is not equal to 3/4, they are not proportional.
3. (5/7 and 7/14): The second ratio (7/14) simplifies to 1/2. Since 5/7 is not equivalent to 1/2, these are not proportional.
4. (21/28 and 12/16): Simplifying both ratios, (21/28) simplifies to 3/4 and so does (12/16). Therefore, these two are proportional.

So, the ratios in option D, (21/28 and 12/16), represent quantities that are proportional.