# Ratios

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## Learn about Ratios from Certified Online Pre-Algebra Tutor

### What is the ratio in math?

A **ratio** gives the relative sizes of two sets but not the actual numbers of objects in those sets. For example, the fact that the ratio of blue marbles to red marbles in a box is 3 to 4 tells us that for every 3 blue marbles there are 4 red marbles; however, it does not tell us the number of blue or red marbles.

The order of terms in a ratio is important. Notice that in the expression **“the ratio of blue marbles to red marbles,”** “blue marbles” came first. This order is important: whichever word comes first; its number must come first as well. If the expression had been **“the ratio of red marbles to blue marbles,”** then the numbers would have been **“4 to 3.”**

Ratios are similar to fractions; they can both be simplified by finding common factors. Always try to divide by the highest common factor.

A ratio may be written as **a: b** or **a/b** or by the phrase **“a to b”**.

A ratio of 1:6 says that the second number is six times as large as the first.

### What is a ratio example?

There are 25 girls and 15 boys in a class. What is the ratio of girls to boys? Give your answer in its simplest form.

The ratio of girls to boys is 25:15

However, both sides of this ratio are divisible by 5

Dividing by 5 gives 5:3

5 and 3 have no common factors (apart from 1).

So the simplest form of the ratio is 5:3

This means there are 5 girls in the class for every 3 boys.

### Check Point

**a)** In a telephone poll, 88 people said they like watching basketball and 70 people said they do not like watching basketball. What is the ratio of the number of people who like watching basketball to the number of people who do not like watching basketball? Give your answer in its simplest form.

**b)** A movie theater sold 62 child tickets. The other 96 tickets it sold were adult tickets. What is the ratio of the number of adult tickets to the number of child tickets? Give your answer in its simplest form.

**c)** Anne’s Ice Cream Shop sold 52 sundaes with nuts and 39 sundaes without nuts. What is the ratio of the number of sundaes with nuts to the number of sundaes without nuts? Give your answer in its simplest form.

**d)** There are 48 men and 102 women participating in a triathlon. What is the ratio of the number of women participating to the number of men participating? Give your answer in its simplest form.

**e)** The sixth-graders at Alice’s school got to visit either the science museum or the history museum. 110 students picked the science museum and 115 students picked the history museum. What is the ratio of the number of sixth-graders who visited the history museum to the number of sixth-graders who visited the science museum? Give your answer in its simplest form.

### Answer key

**a)** 44:35

**b)** 48:31

**c)** 4:3

**d)** 17:8

**e)** 23:22

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