### Numbers: Ratios

### Ratios

In order to make lemonade, we need #1# part concentrate and #5# parts water. This means we always need #5# times as much water as concentrate. We write this as #1 : 5# (pronounced as: 1 to 5) and call this a **ratio.**

With this ratio, we can calculate how much water we need when we have #20# mL of concentrate, namely #5# times as much. We therefore need #5 \times 20# mL #=100# mL of water.

The ratio #20 :100# is therefore equal to #1:5#, since the lemonade proportionally contains the same amount of concentrate as before. When asked for a ratio, we always simplify as much as possible.

In general:

*A ratio between two quantities indicates the relation between one quantity and the other.*

**Examples**

\[\begin{array}{c}1:4 \\ \\ 5:6 \\ \\ 2:3 \\ \\ 8:9 \\ \\ 5:3 \end{array}\]

A simple way of performing calculations involving ratios, is using a ratio table.

We can put a ratio in a **ratio table.**

We put the first number of the ratio in the top row of the table, and the second number in the bottom row.

When we multiply or divide the top row by a number, we also have to do so with the bottom row. The ratio does not change.

We first write #6:78#. We can now divide both #6# and #78# by #6#. Therefore, the ratio is equal to #1 : 13#.

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