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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. Page 1 of 6 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? Page 2 of 6 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? Page 3 of 6 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 Page 4 of 6 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? Page 5 of 6 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 Page 6 of 6