Year 8AC9M8M07

Ratios and Rates in Context

Use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts.

A ratio compares two amounts of the same kind. A rate compares two different kinds. Getting that distinction right decides which method you use.

Method

Ratio: same units, no units in the answer

3:2

Simplify like a fraction.

Rate: different units, units stay

80 \text{ km/h} \qquad \$4{,}50/\text{kg}

The unit is part of the answer.

Unit rate means per one

\frac{\text{total}}{\text{how many}}

Divide to compare two deals fairly.

Scale up by multiplying both parts

Whatever you do to one side, do to the other.

e.g.

\text{Which is better value: } 3\text{ kg for } \$7{,}50 \text{ or } 5\text{ kg for } \$12{,}00?

To compare fairly, find the cost of one kilogram each time. $\text{find the unit rate}$
First deal. $7{,}50 \div 3 = \$2{,}50/\text{kg}$
Second deal. $12{,}00 \div 5 = \$2{,}40/\text{kg}$
Compare the unit rates. Lower is better value. $2{,}40 < 2{,}50$
State the answer in context. $\text{The 5 kg bag is better value.}$

Decide first whether it is a ratio or a rate.

\text{Simplify } 18:24

Answer

3:4

\text{Share } \$140 \text{ in the ratio } 3:4

Answer

\$60 \text{ and } \$80

\text{A car travels } 240 \text{ km in } 3 \text{ hours. Find the speed.}

Answer

80 \text{ km/h}

\text{6 pens cost } \$9. \text{ Find the cost of 10.}

Answer

\$1{,}50 \text{ each} \Rightarrow \$15

\text{Is } 50 \text{ km/h a ratio or a rate?}

Answer

\text{A rate — km and hours are different units.}

\text{A recipe for 4 uses } 300\text{ g flour. How much for 6?}

Answer

450 \text{ g}