Ratios and Rates

Lesson

Our ratio journey so far has taken us through the process of simplifying, using ideas similar to how we simplify fractions. We have also explored a number of applications of ratios where we scaled the ratios up or down to answer questions in context. We have also used tables of values in ratio tables to explore the proportional connection between two quantities.

Another application of ratios can also be seen in converting units, imperial to metric and vice versa.

The ratio of miles to kilometers is $1:1.6$1:1.6. Use this fact to find out how many kilometers are equal to $5$5 miles.

**Think**: The given ratio of $1:1.6$1:1.6 means that $1$1 mile is equal to $1.6$1.6 kilometers. Set up a ratio problem, identifying by what factor each part of the ratio needs to be multiplied to give $5$5 miles.

**Do**:

miles | to | kilometers |

$1$1 | $:$: | $1.6$1.6 |

to get $5$5 miles, we need $5$5 groups of the part representing miles in the ratio | so we also need to multiply the number of kilometers by $5$5 | |

$1\times5$1×5 | $:$: | $1.6\times5$1.6×5 |

$5$5 | $:$: | $8$8 |

So $5$5 miles is equivalent to $8$8 kilometers.

$1$1 gallon is around $3.8$3.8 liters.

**a) **State this as a ratio of liters to gallons, in the form $a:b$`a`:`b`. Give your answer in simplest form.

**Think**: We want a ratio that compares the number of liters to the numer of gallons.

**Do**: Litres:Gallons = $3.8:1$3.8:1

Simplest form is without fractions or decimals:

$3.8$3.8 | $:$: | $1$1 | multiply both parts by $10$10 to remove the decimal |

$38$38 | $:$: | $10$10 | divide both parts by common factor of $2$2 |

$19$19 | $:$: | $5$5 | this is in simplest form |

This means that $19$19 litres is equivalent to $5$5 gallons.

**b)** How many liters would a $15$15 gallon vat hold?

**Think**: Use the conversion ratio.

**Do**:

Litres | to | Gallons | |

$19$19 | $:$: | $5$5 | for $15$15 gallons we need to multiply the $5$5 "gallons" parts by $3$3. |

$19\times3$19×3 | $:$: | $5\times3$5×3 | so we need to multiply both parts of the ratio by $3$3 |

$57$57 | $:$: | $15$15 |

So $15$15 Gallons is equivalent to $57$57 Litres.

The ratio of kilograms to ounces is $1:2.2$1:2.2. Use this fact to complete the workings below for finding out how many ounces are equal to $10$10 kilograms.

$1$1 **:**$2.2$2.2 × $\editable{}$ × $10$10 $\editable{}$ **:**$\editable{}$

$1$1 foot is equal to around $0.3$0.3 meters.

State this as a ratio of feet to meters, in the form $a:b$

`a`:`b`. Write your answer in simplest form.How many meters would a $100$100 foot garden be?