Unit 1: Ratio, Rate, & Proportion
Topic B: Rates
When a ratio is used to compare two different kinds of measure (e.g. apples and oranges, or meters and hours), it is called a rate. The denominator must be 1.
Example A
A car can drive 725 km on 55 L of gas. What is the rate in km per L? The ratio of this is [latex]\dfrac{725\text{ km}}{55\text{ L}}[/latex]. Find the rate by making the denominator 1.
Divide [latex]\dfrac{725}{55} \div \left(\dfrac{55}{55}\right) = \dfrac{725\div55}{55\div55}=\dfrac{13.18}{1}=13.18[/latex]
The rate is 13.18 km/L.
Example B
Sue bought 10 lb of oranges for $4.99. What is the rate in cents per pound? The ratio is [latex]\dfrac{$4.99}{10\text{ lb}}=\dfrac{499\text{ cents}}{10 \text{ lb}}[/latex]. Find the rate by making the denominator 1.
Divide [latex]\dfrac{499}{10} \div \left(\dfrac{10}{10}\right) =\dfrac{499\div10}{10\div10}=\dfrac{49.9}{1}=49.9[/latex]
The rate is 49.9 ¢/lb.
When talking about rate, use the word ‘per’.
In example A, say: “The fuel economy of the car is 13.18 kilometres per litre”.
In example B, say: “The oranges cost 49.9 cents per pound”.
Example C
It takes 60 ounces of grass seed to plant 30 m2 of lawn. What is the rate in ounces per square metre (m2)? The ratio is [latex]\dfrac{60\text{ oz}}{30\text{ m}^2}[/latex]. Find the rate by making the denominator 1.
Divide [latex]\dfrac{60}{30} \div \left(\dfrac{30}{30}\right) = \dfrac{60\div30}{30\div30}=\dfrac{2}{1}=2[/latex]
The rate is 2 oz/m2, or 2 ounces per square metre.
Exercise 1
Write the following ratios as rates, comparing distance to time.
- 120 km, 3 hours
- 27 km, 9 hours
- 203 km, 29 seconds
- 444 km, 48 seconds
Answers to Exercise 1
- 40 km/hour
- 3 km/hour
- 7 km/second
- 9.25 km/second
Exercise 2
Write the following ratios as rates.
- A leaky faucet can lose 52 litres of water in a week. What is the rate of litres lost per day? (round to two decimal places)
- A ratio of distance travelled to time is called speed. What is the rate (speed) in kilometres per hour (km/h)?
- 45 km, 3 hours
- 129 km, 1.5 hours
- 65 km, 13 hours
- Vancouver Island has a population of 734,860, and a land mass of 32,134 square kilometres. What is the rate of number of people per square kilometre? (This is called population density.) Round your answer to the nearest whole number.
- At rest, the heart beat of a mouse is 30,000 beats per 60 minutes. What is the rate of beats per minute?
Answers to Exercise 2
- 7.43 L/day
-
- 15 km/hour
- 86 km/hour
- 5 km/hour
- 23 people/km2
- 500 beats/minute
Topic B: Self-Test
Mark /7 Aim 6/7
- Write the definition.
(1 mark)- Rate
- Write the following ratios as rates. Round people to the nearest person.
(6 marks)- 12 cups water, 3 cups sugar
- 72 metres, 24 seconds
- 1,365,000 people, 4,000 km2
- 5,000 cars on the road, 250 bikes on the road
- 12 cups of flour, 12 tsp. of baking powder
- 8 litres of gas, 2 litres of oil
Answers to Topic B Self-Test
- A rate is used when a ratio compares two different kinds of measure, and when