Simplify and compare rates

Lesson

Rates

A rate is a ratio between two measurements with different units. A common example of a rate is speed (which is written in kilometres per hour or km/h). You can see that this describes a relationship between two measurements- kilometres and hours.

Examples

Question 1

Evaluate: If I drive at $55$55km/hour, how far will I travel in $4$4 hours?

Think: $55$55km represents the distance traveled in one hour, so to work out how far I went in $4$4 hours, I would need to multiply this distance by $4$4.

Do: $55\times4=220$55×4=220km

These questions don't always use multiplication. Sometimes we need to use division.

question 2

What is the speed of a car that travels 56km in 7 hours?

Question 3

Evaluate: If Lee paid $\$11.8511.85 for $3$3kg of apples, how much did he pay per kilogram?

Think: To find out what $1$1kg costs, we need to divide the weight by $3$3. So we also need to divide the cost by $3$3.

Do:$11.85\div3=\$3.95$11.85÷​3=$3.95 $/kg$/kg

Question 4

Convert 300 mL/h to mL/min.

Question 5

In 2011, the literacy rate in Cuba was 98 people for every 100 in the population. For a town with a population of 83 000, how many literate people would you expect?

Outcomes

9P.NA1.05

Solve problems involving ratios, rates, and directly proportional relationships in various contexts (e.g., currency conversions, scale drawings, measurement), using a variety of methods (e.g., using algebraic 15 20 x 4 reasoning, equivalent ratios, a constant of proportionality; using dynamic geometry software to construct and measure scale drawings)