Ratios and Rates

Lesson

In Keeping it Simple, we introduced the concept of simplifying ratios. Remember what we are trying to do is express ratios in the lowest possible whole numbers. So if our ratios have fractions, decimals, numbers with common factors or mixed units of measurements, we can simplify them.

Here's an example using decimals

**Question**: Simplify the ratio $0.72:1.8$0.72:1.8

**Think:** If we multiply both numbers by $100$100, they will both be whole numbers, then we can simplify them if we can.

**Do:**

$0.72:1.8$0.72:1.8 | $=$= | $72:180$72:180 | we can divide both numbers by $9$9 |

$=$= | $8:20$8:20 | we can divide both numbers by $4$4 | |

$=$= | $2:5$2:5 |

Let's look at an example that uses fractions.

Simplify the ratio $\frac{2}{7}$27:$\frac{5}{7}$57

The same principles apply, even if only one number is a fraction or decimal.

**Question**: Simplify the ratio $3:\frac{1}{5}:2$3:15:2

**Think:** We can multiply all the numbers by $5$5 to make them whole numbers, then we can simplify them if we can.

**Do: **

$3:\frac{1}{5}:2$3:15:2 | $=$= | $15:1:10$15:1:10 | multiply all parts by $5$5 to remove the fraction |

this answer is as simplified as we can get. |

What about one with mixed units of measurement?

Write $32$32 minutes to $3$3 hours as a ratio (make sure your answer is in it's simplest form).

Apply direct and inverse relationships with linear proportions

Apply numeric reasoning in solving problems