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.
2. A ratio of distance travelled to time is called speed. What is the rate (speed) in kilometres per hour (km/h)?
a. 45 km, 3 hours
b. 129 km, 1.5 hours
c. 65 km, 13 hours
Answers to Exercise 2
1. 7.43 L/day
2a. 15 km/hour
2b. 86 km/hour
2c. 5 km/hour
3. 23 people/km2
4. 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
1. A rate is used when a ratio compares two different kinds of measure, and when the denominator is 1.
2.
-
- 4 cups of water/cups of sugar
- 3 m/second
- 341 people/km2
- 20 cars/bike
- 1 cup flour/tsp baking powder
- 4 litres gas/litre oil