Question

Please help :)

Show all the steps that you use to solve this problem.

Are the ratios 84/105 and 128/160 proportional?

Give two different reasons to support your answer

Answer 1

The ratios 84/105 and 128/160 are proportional

Solution:

Given, two ratios are
`(84)/(105)` and
`(128)/(160)`

We have to give two different reasons to support the answer.

Reason 1:

Now, we know that, numerators and denominators should be proportional to be two fractions in proportion.

`\text { Then, } (84)/(128)=0.65625 \text { and } (105)/(160)=0.65625`

So numerators and denominators are in proportion, then given two fractions are proportion.

Reason 2:

Now, values of two fractions must be equal:

`\rightarrow (84)/(105)=(128)/(160) \rightarrow 84 * 160=105 * 128 \rightarrow 13440=13440`

So, values of two fractions are equal, then they are in proportion.

Hence, the given two fractions are in proportion.