Question

Which two ratios form a proportion?

Responses
A 12/15 and 5/4
B 15/12 and 5/4
C 6/5 and 4/5
D 5/6 and 4/5

Answer 1

Step-by-step explanation: We will determine if ratios are proportional using cross multiplication.

first, we will check option (a)

12/15 =5/4

12*4 = 15*5

48 is not equal to 75. So, these are not proportional.

now, we will check option (b)

15/12 = 5/4

15*4 = 12*5

60 = 60.

as the left-hand side is equal to the right-hand side.

So, option (b) is correct.

Answer 2

`\textsf{B)} \quad (15)/(12)\; \textsf{and}\;(5)/(4)`

Explanation:

If two fractions are equal, they form a proportion.

Therefore, to determine if two ratios form a proportion, rewrite the fractions so that their denominators are the same, then compare.

`\textsf{A)}\quad (12)/(15)\; \textsf{and}\;(5)/(4) \implies (12 * 4)/(15* 4)\; \textsf{and}\;(5* 15)/(4* 15)\implies (48)/(60)\; \textsf{and}\;(75)/(60)`

As the two fractions are not equal, they do not form a proportion.

`\textsf{B)} \quad (15)/(12)\; \textsf{and}\;(5)/(4)\implies (15)/(12)\; \textsf{and}\;(5 * 3)/(4 * 3)\implies (15)/(12)\; \textsf{and}\;(15)/(12)`

As the two fractions are equal, they form a proportion.

`\textsf{C)} \quad (6)/(5)\; \textsf{and}\;(4)/(5)`

The denominators of these two fractions are already the same.

Therefore, as the two fractions are not equal, they do not form a proportion.

`\textsf{D)} \quad (5)/(6) \; \textsf{and}\;(4)/(5)\implies (5* 5)/(6* 5) \; \textsf{and}\; (4* 6)/(5* 6)\implies (25)/(30)\; \textsf{and}\;(24)/(30)`

As the two fractions are not equal, they do not form a proportion.