Ratio of 35 cents to $2 Step by Step

Step by step

The question

Question: write the ratio of 35 cents to 2 dollars in its simplest form.

35 cents : $2

Careful!

The units are not the same: cents and dollars.

35 to 2 would compare different things.

Careful: not 35 : 2 ✗

1 Same units

A ratio only compares amounts in the same unit.

We change to the smaller unit, cents, so there are no fractions.

1 dollar is 100 cents.

1 dollar = 100 cents

So 2 dollars is 2 times 100: 200 cents.

= $2 = 2 × 100 cents = 200 cents

2 Drop the units

Now the ratio is 35 cents to 200 cents.

= 35 ~~cents~~ : 200 ~~cents~~

Both are in cents.

The same units cancel, so we cross them out.

That leaves 35 to 200.

= 35 : 200

3 Simplify

35 and 200 can both be divided by 5.

We divide both parts by 5.

The ratio stays the same.

= 35 ÷ 5 : 200 ÷ 5

35 divided by 5 is 7.

200 divided by 5 is 40.

So the ratio is 7 to 40.

= 7 : 40

4 Check

Let's check: times each part by 5.

We get 35 cents and 200 cents again.

7 × 5 = 35 cents, 40 × 5 = 200 cents

And 200 cents divided by 100 is 2 dollars, as in the question.

So the answer is right!

200 cents = 200 ÷ 100 = $2

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.

Answer