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Grade 9

Simplify and compare 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.


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 $\$11.85$$11.85 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?



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)

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