Question

Are the ratios 84/105 and 128/160 proportional? Give two different reasons to support your answer.

Answer 1

We have been given two ratios and we are supposed to compare our ratios whether they are proportional or not.

1. We will reduce our fractions to compare our ratios. Let us simplify each of our given fractions.

$\frac{84}{105}$

Let us divide numerator and denominator with greatest common factor. We can see that 21 is GCF of our ratio.

$\frac{4}{5}$

Now we will simplify our second ratio.

$\frac{128}{160}$

GCF of our fraction is 32. Upon dividing our fraction by 32 we will get,

$\frac{4}{5}$

We can see that our both ratios are similar.

2. Now we will find decimal values of our fractions.

$\frac{84}{105}=0.8$

$\frac{128}{160}=0.8$

We can see that $0.8=0.8$.

Therefore, we can say that our ratios are proportional.