# Are 84/105 and 128/160 proportional?

## Question:

Are {eq}\frac {84}{105} {/eq} and {eq}\frac {128}{160} {/eq} proportional?

## Proportions:

In mathematics, if two ratios have the same value, then we say that they are proportional. A proportion is an equation that shows that two ratios, represented as fractions, are equal. We can determine if two ratios, represented as fractions are proportional using the fact that {eq}\frac{a}{b}=\frac{c}{d} {/eq} if and only if ad = bc.

Yes, the two give fractions are proportional. To determine if {eq}\frac{84}{105} {/eq} and {eq}\frac{128}{160} {/eq} are proportional, we can use our fact regarding proportions. That is, {eq}\frac{84}{105}=\frac{128}{160} {/eq} if and only if 84 × 160 = 105 × 128. Thus, we check to see if 84 × 160 is equal to 105 × 128. If it is, the the two fractions are proportional. If it is not, then the two fractions are not proportional.

• 84 × 160 = 13,440
• 105 × 128 = 13,440

We see that both of the products equal 13,440, so {eq}\frac{84}{105}=\frac{128}{160} {/eq}, and we have that the two fractions are proportional. 