The mixing ratio is a unique form of ratio between two quantities. The order is very important, as it tells you what you want more of and what you want less of. If you have a mixing ratio between pure squash and water, that’s not the same as the mixing ratio between water and squash. You write mixing ratios with a colon, not as a ratio. If you are mixing squash and water in the ratio 1 to 4, you write the mixing ratio as

$$1:4.$$ |

You need to read the text on the bottle to see what you need 1 part of and what you need 4 parts of.

Rule

The mixing ratio between $A$ and $B$ is

$$x:y,$$ |

which means $x$ parts $A$ and $y$ parts $B$.

As the mixing ratio only tells you something about how many parts you need of each thing, you need to add the two numbers together to get the total number of parts. A mixing relationship of $1:4$ has 1 part squash and 4 parts water, which is $1+4=5$ parts in total. All the parts have the same size.

Example 1

**You are mixing squash and water with a mixing ratio of $1:4$. How much water do you need if you have $\text{}2\text{}\phantom{\rule{0.17em}{0ex}}\text{dL}$ squash? **

You look at the mixing ratio first. You should use 4 times as much water as squash. As you have $2$ dL squash, you need

$$2\phantom{\rule{0.17em}{0ex}}\text{dL}\cdot 4=8\phantom{\rule{0.17em}{0ex}}\text{dL}$$ |

of water. In total you get

$$2\phantom{\rule{0.17em}{0ex}}\text{dL}+8\phantom{\rule{0.17em}{0ex}}\text{dL}=10\phantom{\rule{0.17em}{0ex}}\text{dL}=1\phantom{\rule{0.17em}{0ex}}\text{L}$$ |

of finished squash.

Example 2

**John is mixing oil and gas to make fuel for his chainsaw. His mixing ratio is $1:25$. How much oil does he need if he has $\text{}5\text{}\phantom{\rule{0.17em}{0ex}}\text{L}$ of petrol? **

As he needs 25 times more gas than oil, it can be a good idea to change the numbers into dL first. John has $5\phantom{\rule{0.17em}{0ex}}\text{L}=50\phantom{\rule{0.17em}{0ex}}\text{dL}$ of gas.

$$\frac{50\phantom{\rule{0.17em}{0ex}}\text{dL}}{25}=2\phantom{\rule{0.17em}{0ex}}\text{dL}$$ |

This means that John needs to mix in $2$ dL of oil to make the fuel.

Example 3

**You are mixing light yellow paint, and want to do it by mixing yellow paint with white paint. You mix a total of $\text{}14\text{}\phantom{\rule{0.17em}{0ex}}\text{dL}$ in the ratio $2:5$. You then discover that you should have mixed it in the ratio $3:5$ instead. What can you do to fix the ratio? **

You already mixed the paint in the ratio $2:5$. That means you have 7 parts in total. You had $14$ dL of paint, which means there are $\frac{14}{7}=2\phantom{\rule{0.17em}{0ex}}\text{dL}$ per part. If you then add $2$ dL of yellow paint to the mix, you will have $1+7=8$ parts in total, where 3 of the parts are yellow and 5 of the parts are still white. That makes the mixing ratio $3:5$, just like you wanted.

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