06 - Rates, Ratios and Proportions PDF

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6 - Rates, Ratios and Proportions

MPM1D – Review

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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6 - Rates, Ratios and Proportions

MPM1D – Review

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) $59.00 for 4 hours of cutting laws ($/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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6 - Rates, Ratios and Proportions

MPM1D – Review

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

6 - Rates, Ratios and Proportions

MPM1D – Review

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)

 

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

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? f) A recipe for making brownies uses 4 cups of sugar to make 12 brownies. How much sugar is required to make 60 brownies?

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6 - Rates, Ratios and Proportions

MPM1D – Review

Answers 1. a) 3:7

b) 7:4

c) 3:2

2. a) 1:2

b) 2:5

c)



d) 4:3:5



3. a) 4

b) 1:6:3 = 3:18:9

4. a) $3.16 per can

b) $31 per day

c) 72 beats/min

d) 0.15 km/min

e) 125 ml/person

f) 3.5 km/hr

g) $10.75 per hr

h) 225 g per cake

5. a) $4.75 per sandwich

b) $40.00 per hour

6. a) 4:3

b) 8:1

c) 1:5

b) Nicole = $9.75/hr

c) 39:12

7. a) 150°

Leon = $9.60/hr Nicole is paid more d) $9.71/person (35)

e) 36 kg

f) 20 cups

$10.80/person (40) Renting for 40 is better

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