## Equivalent Ratios

#### What are Equivalent Ratios?

Ratios that are equal to each other are called equivalent ratios.

*Examples:*- 16 : 4 = 8 : 2 = 4 : 1
- 1 : 3 = 3 : 6
- 4 : 25 = 16 : 100 = 160 : 1000

#### 1. Are the ratios 8 : 4, 4 : 2 and 2 : 1 equivalent?

Let's suppose that we have 8 red coins and 4 blue coins.

The ratio of the number of red coins to the number of blue coins is

The ratio of the number of red coins to the number of blue coins is

**8: 4**.
Now, let's rearrange the coins into stacks of 2 coins each as shown below.

Now, the ratio of the number of red coins to the number of blue coins is

Now, the ratio of the number of red coins to the number of blue coins is

**4 : 2**.
Finally, let's put the coins into stacks of 2 coins each as shown below.

The new ratio of the number of red coins to the number of blue coins is

The new ratio of the number of red coins to the number of blue coins is

**2 : 1**.For every 8 red coins there are 4 blue coins.

Or

For every 4 red coins there are 2 blue coins.

Or

For every 2 red coins there is 1 blue coin.

The ratios 8 : 4, 4 :2 and 2 : 1 are, therefore,

**equivalent ratios**.

2:1 is the

**simplest form**of 8:4.

**Note:**

To get the equivalent of a ratio, multiply / divide all the terms of the ratio by the same number.