Equivalent Ratios

What are equivalent ratios?

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

Examples:

  1. 8 : 4 = 4 : 2 = 2 : 1

  2. 1 : 3 = 3 : 6

  3. 4 : 25 = 16 : 100 = 160 : 1000

Show that the ratios 8 : 4, 4 : 2 and 2 : 1 are 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 8: 4.

Let's put the coins into stacks of 2 coins each.



The ratio of the number of red coins to the number of blue coins is 4 : 2.

Now, let's put the coins into stacks of 4.



The ratio of the number of red coins to the number of blue coins is 2 : 1.

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



For every 8 red coins there are 4 blue coins.

Or

For every 4 red coins there are 2 blue coins.

Or

2:1 is the simplest form of 8:4.
For every 2 red coins there is 1 blue coin.


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