# Ratios

### What are Ratios?

There will be questions on the ACT math exam on ratios.

Ratios are expressed by using the colon.

So, a ratio of 2 to 100, for example, is expressed as follows:

2 : 100

The number before the colon expresses one subset of the total amount of items.

The number after the colon expresses a different subset of the total.

In other words, when the number before the colon and the number after the colon are added together, we have the total amount of items.

Now try these problems.

1) In a shipment of 100 mp3 players, 1% are faulty.

What is the ratio of non-faulty mp3 players to faulty mp3 players?

A. 1: 100

B. 99: 100

C. 1: 99

D. 99: 1

E. 1: 499

This problem is asking for the quantity of non-faulty mp3 players to the quantity of faulty mp3 players.

Therefore, you must put the quantity of non-faulty mp3 players before the colon in the ratio.

In this problem, 1% of the players are faulty:

1% × 100 = 1 faulty player in every 100 players

100 − 1 = 99 non-faulty players

As explained above, the number before the colon and the number after the colon can be added together to get the total quantity.

So the ratio is:

99: 1

2) In class of 50 children, 3 children have red hair.

What is the ratio of red-haired children to non-red-haired children?

A. 1: 3

B. 3: 50

C. 3: 47

D. 1: 53

E. 3: 53

This problem is asking for the ratio of red-haired children to non-red-haired children.

Therefore, you must put the quantity of red-haired children before the colon in the ratio.

In this problem, 3 of the children in the class have red hair.

Then calculate the amount of children that do no have red hair

50 − 3 = 47 children who do not have red hair

Remember that the number before the colon and the number after the colon can be added together to get the total quantity.

So the ratio is:

3: 47

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