Question

Do the following ratios have a proportional relationship? Determine proportionality by creating equivalent fractions.

Answer 1

a) Proportional, proportion of 4/3.

b) `Proportional, proportion of 3/4

Explanation:

Ratios are proportional if the result of their division is 1.

Division of fractions: Multiplication of the numerator by the inverse of the denominator.

Item a:

`((4)/(3))/((12)/(9))=(4)/(3)\ast(9)/(12)=(4\ast9)/(3\ast12)=(36)/(36)=1`

So yes, they are proportional at the ratio of the 4/3.

Item b:

`((6)/(8))/((9)/(12))=(6)/(8)\ast(12)/(9)=(6\ast12)/(8\ast9)=(72)/(72)=1`

So yes, they are proportional at the ratio of 6/8. This fraction can be simplified by 2, so 3/4.