Ratios and Rates

Lesson

In Looking at Relationships Between Different Groups we discussed how to express and simplify ratios. Once you understand these concepts, you can use it to find unknown values in related ratios.

Remember we can write ratios as fractions to help us find unknown values in ratios.

Find the value of $a$`a` if $a:8=384:48$`a`:8=384:48

Ratios tell us about the relative sizes of two or more values. They are often used in everyday life, whether it's for dividing up money, cooking or mixing cement! So knowing how to apply your knowledge about ratios is really important. Remember that the order that the words are written in the question corresponds to the order of the values in the ratio so don't jumble them around.

**Question**: A piece of rope is cut up in the ratio $7:10:3$7:10:3. If the rope is $20$20m long, how long is each section (name them $A$`A`, $B$`B` and $C$`C`)?

**Think:** The total number of parts is $20$20 $\left(7+10+3\right)$(7+10+3). So to work out the value of one part, we calculate $20\div20=1$20÷20=1

**Do:**

$A$A |
has | $7$7 parts |

$=$= | $7\times1$7×1 | |

$=$= | $7$7 m | |

$=$= | ||

$B$B |
has | $10$10 parts |

$=$= | $10\times1$10×1 | |

$=$= | $10$10 m | |

$C$C |
has | $3$3 parts |

$=$= | $3\times1$3×1 | |

$=$= | $3$3 m |

Let's look at another question.

**Question**: The ratio of girls to boys in a school is $3:5$3:5. If there are $180$180 girls in the school, how many boys are there?

**Think:** How do these numbers relate? The $3$3 in the ratio corresponds to $180$180 girls (it's just $60$60 times bigger) and the $5$5 corresponds to the unknown value, which we'll call $x$`x`. So to work out the value of $x$`x`, we work calculate $5\times60=300$5×60=300.

**Do:** There are $300$300 boys.

Increase $9$9 in the ratio of $10:3$10:3.

Decrease 10km in the ratio $7:8$7:8.

Apply direct and inverse relationships with linear proportions

Apply numeric reasoning in solving problems