# Intro to Ratios

## Overview

Understanding Ratios

A **ratio** expresses the relationship between two quantities.

Look at the shapes below. We can see that there are some hearts as well as some

stars, but what is the ratio of stars to hearts?

__Step 1__: Calculate the first quantity

First we need to calculate the number of stars because the question is asking the

ratio of “stars” to “hearts”.

There are

**2**stars

__Step 2__: Calculate the second quantity

Next, we need to calculate the number of hearts.

There are

**3**hearts

__Step 3__: Express the relationship between the first and second quantities

*The relationship can be expressed as:*

The ratio of stars to hearts is

We can also say:

For every **2 stars** there are **3 hearts**

or

**2** to **3**

Let’s look at a more challenging example.

What is the ratio of stars to hearts?

__Step 1__: First we calculate the number of stars, which is

**3**.

__Step__: Next we calculate the number of hearts, which is

**2****6**.

__Step 3__: Now, we express the relationship as

__Step 4__: We can simplify the ratio just as we simplify fractions.

The common factor is **3**. So, the ratio of stars to hearts is

__Step 5__: You can check your answer by looking at the quantities

We can see that for every **1** star, there are **2** hearts ✓

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###
What is the ratio of apples to oranges?

Answer
4 to 3

There are 4 apples and 3 oranges. This ratio cannot be simplified.

What is the ratio of apples to oranges?

4 to 3

There are 4 apples and 3 oranges. This ratio cannot be simplified.

###
What is the ratio of fish to cats?

Answer
2 to 1

There are 6 fish and 3 cats. The ratio 6 : 3 can be simplified to 2 : 1

What is the ratio of fish to cats?

2 to 1

There are 6 fish and 3 cats. The ratio 6 : 3 can be simplified to 2 : 1

###
What is the ratio of cats to dogs?

Answer
7 : 2

There are 7 cats and 2 dogs. This ratio cannot be simplified.

What is the ratio of cats to dogs?

7 : 2

There are 7 cats and 2 dogs. This ratio cannot be simplified.

###
What is the ratio of carrots to ice cream cones?

Answer
5 : 2

There are 5 carrots and 2 ice cream cones. This ratio cannot be simplified.

What is the ratio of carrots to ice cream cones?

5 : 2

There are 5 carrots and 2 ice cream cones. This ratio cannot be simplified.

###
What is the ratio of donuts to candy?

Answer
1 : 1

There is one donut and 1 candy.

What is the ratio of donuts to candy?

1 : 1

There is one donut and 1 candy.

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