Download 5 - Rates, Ratios and Proportions

MPM1D – Review
874000960
Date: _________________________
Rates, Ratios and Proportions
Ratios
A ratio compares two numbers with the same units.
We can write a ratio in three different ways: in words, in colon form (most common), or
in fraction form.
 The order of terms is very important!
 A ratio can have more than two terms!
 Since all of the terms in a ratio have the same units, a ratio does not have units.
Examples:
1. Determine the ratio of consonants to vowels for each word.
Word
In Words
In Colon Form
In Fraction Form
Elephant
5 to 3
5:3
5
3
Pumpkins
2. Write the following ratios in 3 different ways (remember that ratios have the same
units!):
a) 2 m to 13 cm
b) 2 years to 34 months
3. The wingspan of a model plane is 35 cm. The wingspan of the actual plane is 49 m.
Write the ratio of the model’s measurements to the actual plane’s measurement.
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MPM1D – Review
874000960
Rates & Unit Rates
A rate compares two numbers expressed in different units.
A unit rate is a rate in which the second term is 1.


Rates are commonly written in fraction form.
Since the terms in a rate have different units, a rate has units.
Examples:
1. Express each of the following as a unit rate.
a) $39.00 for 6 hours of cutting laws ($/hr) b) 240 m walked in 10 minutes (cm/s)
2. A police car travels 9.5 km in 5 minutes.
a) What is this speed in km/h?
b) At this speed, how far will the police car travel in 1.5 hours?
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MPM1D – Review
874000960
Equivalent Ratios and Proportions
Ratios that make the same comparison are equivalent ratios.
A proportion is a statement that two ratios are equal to each other.
Examples:
1. Find an equivalent ratio.
a) 24 : 18
b) 3 : 4
2. Are the ratios in each pair equivalent?
a) 3 : 5 and 50 : 75
b) 12 : 8 and 3 : 2
3. Mr. Lee wants to make up some cleaning solution to clean his
whiteboards. His grandmother gave him the recipe shown to
the right. How much ammonia is required to make 3 L of
cleaner?
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Whiteboard Cleaner
6 parts ammonia
4 parts washing soda
140 parts water
MPM1D – Review
874000960
Homework
1. Express each as a ratio.
a) 3 pucks to 7 sticks
b) 7 foxes to 4 coyotes
c) 6 perch to 4 pike
2. Write each ratio in lowest terms.
a) 4 : 8
b) 8 : 20
c)
15
25
d) 24 : 18 : 30
3. Write the missing term(s) for the following.
a) 2 : 5 = ___ : 10
b) 1 : 6 : ____ = 3 : ____ : 9
4. Write as a unit rate:
a) $9.48 for 3 cans of juice
b) $186 for a 6-day car rental
c) 432 heartbeats in 6 minutes
d) jogging 1.8 km in 12 minutes
e) 750 mL of juice for 6 people
f) skiing 14 km in 4h
g) $129 for 12 h of work
h) 900 g of batter for 4 cakes
5. Find the unit price. Round to the nearest cent.
a) $28.50 for 6 sandwiches
b) $100.00 for 2.5 hours of golf lessons
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MPM1D – Review
874000960
6. Write as a ratio in simplest form (remember: ratios have the same units!)
a) 1 min to 45 s
b) 2 kg to 250 g
c) 73 days to 1 year
7. Applications and Problem Solving:
a) The Earth spins 360˚ about its axis in 24 hours. How many degrees does it spin
in 10 hours?
b) Nicole earned $78 for 8 hours of house painting. Leon earned $115.20 for 12
hours of work. Who had the higher rate of pay and by how much?
c) One year 78% of Canadian households owned cars and 24% owned air
conditioners. Write a ratio of households with cars to households with air
conditioners as a ratio in lowest terms.
d) Which of the following is the better value, $340 for a bus for 35 people or $432
for a bus for 40 people?
e) The body of a 50 kg woman contains 30 kg of water. What is the mass of water
in a 60 kg woman?
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MPM1D – Review
874000960
f) A recipe for making brownies uses 4 cups of sugar to make 12 brownies. How
much sugar is required to make 60 brownies?
Answers:
1.
a) 3:7
b) 7:4
c) 3:2
2.
a) 1:2
b) 2:5
c)
3.
a) 4
b) 1:6:3 = 3:18:9
4.
a) $3.16 per can
e) 125 ml/person
b) $31 per day
f) 3.5 km/hr
5.
a) $4.75 per sandwich
6.
a) 4:3
7.
a) 150°
d) $9.71/person (35)
$10.80/person (40)
Renting for 40 is better
3
5
d) 4:3:5
c) 72 beats/min
g) $10.75 per hr
d) 0.15 km/min
h) 225 g per cake
b) $40.00 per hour
b) 8:1
c) 1:5
b) Nicole = $9.75/hr
Leon = $9.60/hr
Nicole is paid more
c) 39:12
e) 36 kg
f) 20 cups
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