= 2 = x 3 24

Solve as an equivalent fraction: 3 8 = 24 so 2 8 = 16; Sarah played 16 gamesSolve using cross multiplication3x = 2 243x = 48x = 16

Name: _______________________________ Date: _________ Class: _____

Ratio, Proportion, Rates and ScaleRatios are used to compare two or more things in quantity. Ratios can be written several different ways: A:B A/B “A to B”

Ratio problems can be classified as part:part, part:whole or comparing three or more quantities. No matter what kind of ratio problem you are solving, however, the key is to keep things balanced. It is sometimes easier to keep things balance if you use words, symbols or pictures.

1. Comparing Part to Part

Sarah and George were comparing their statistics for basketball season. For every two games that Sarah won, George won 3. If George won 24 games, how many games did Sarah win? Let equal the number of games Sarah won

and equal the number of George won

Sarah was flipping through the catalogues and saw a beautiful statue that she wanted to buy. The catalogue stated that the picture was 45% of the original size. Before she bought the statue, Sarah decided she must first find out the actual size. She measured the picture and found out it was 12 cm tall. How big is the actual statue? So the question reads, if 12 cm is 45%, how many cm equals 100%.

Let x = actual size size 12 cm = x cm 12 100 = 45 x

% 45% 100% 1200 = 45x 45 45

x ≈ 26.6 cm or 27 cm

2 = x 5 87

Solve using estimation and fractions by rounding 87 to 85.

85 ÷ 5 = 17 so 2 17 = 34; Sarah made 34 free throws

Solve using cross multiplication2 87 = 5 x174 = 5x 5 5

174÷5 = 34.8

=

2. Comparing Part to Whole

You can also solve problems by creating a fraction that shows the part over the whole.

Sarah made 2:5 free throws. If she attempted 87 free throws this season, how many did she make?

Let equal the number of successful free throws

and equal the total number of free throws attempted.

Sarah was flipping through the catalogues and saw a beautiful statue that she wanted to buy. The catalogue stated that the picture was only 45% of the original size. Before she bought the statue, Sarah decided she must first find out the actual size. She measured the picture and found out it was 12 cm tall. How big is the actual statue? So the question reads, if 12 cm is 45%, how many cm equals 100%. (Remember, the whole is always equal to 100%)

Let x = actual size % and size 45% = 45 cm 12 100 = 45 x

100% size 100% x cm 1200 = 45x 45 45

x ≈ 26.6 cm or 27 cm

Did you notice that no matter how you set up the problem, it was still 12 100 = 45 x ?3. Comparing Three Ratios

George is making fruit punch for the student council dance. The recipe calls for 3 parts pineapple juice to 2 parts apple juice to 1 part orange juice. If he plans on using 45 cups of pineapple juice, how much apple juice and orange juice does he need?

4. Ratios as RatesRates are a special kind of fixed ratio and usually occur in single units, for example the kilometers per hour, students per class, etc. Just as with all ratio problems, it helps to set up the comparison using words first.

If a motorboat travels at a steady speed of 35 km per hour, how far can it travel in 5 hours? Let x = total number of km.

Kilometers 35 km = x km 35 5 = 1 x Hour 1 hr 5 hr 175 = x

5. Ratios as ScaleScale is another special kind of ratio. Maps and models are made to scale.

If 1 cm = 45 km on a map, how many km does 6.7 cm equal? Let x = the total number of km.

cm 1 cm = 6.7 1 x = 45 6.7km 45 km x km x = 301.5

Name: _________________________________ Date: _______ Class: ______

MYP Unit: Proportional ThinkingMYP Question: How does it compare?AOI: Environments

Basic Ratio Problem Set 2

3 = 45 245 = 3x 2 x 90 = 3x 30 = x

45

y

3 = 45 1 45 = 3y 1 y 45 = 3y 15 = y

=

=

1. In a taste test, 780 students preferred mechanical pencils and 220 preferred regular pencils. What is the ratio of preference for mechanical pencils to regular pencils? What percent of students preferred mechanical pencils?

2. Sam has 240 marbles, and 48 of them are red. What is the ratio of marbles to red marbles?

3. The cm:km scale of a map reads 1:125,000. If two cities are 2.4 cm apart, how many km are they apart?

4. In a group of 100 people, the ratio of men to women of 1:3. How many women are there in the group?

5. Two bags contain the same number of marbles. In Bag 1, the ratio of black marbles to white marbles is 4:3. In the Bag 2, the ratio is 3:2. Which bag contains more black marbles?

6. How many meters would you travel in 15 minutes at 62 km/hour?7. Which car gets the better gas mileage rate (hint – find the km/L for each car)

a. Nissan Sentra 1850 km 155.4 L of gasb. Honda Civic 2130 km 100.11 L of

gasc. Lincoln Zephyr 1980 km 235.62d. Mazda 3 1320 km 120.12e. Toyota Highlander 1750 km 222.25

8. If apples are on sale at 5 apples for 320 yen, how much would 8 apples cost?9. Express the following statements as rates.

Example: Customer service department received 40 calls in 60 min – call:min = 1:1.5

a. Peter reads 40 pages in 2 hoursb. A train travelled at 138 km in 60 min.c. A car travelled at 30 km in 20 min.d. A plane flew 210 km in 15 min.

10. Fred exchanged 52,320 yen and received $650. What was the exchange rate?

11. When Sarah exchanged $325, she received 26,065 yen. George exchanged $510 and received 41,004 yen. Who got the better exchange rate?

12. If it took Ms. Montague 45 minutes to write 18 questions, how long will it take her to write 30 questions?

13. Cat food is on sale at the store. 900 grams costs 1550 yen and 1500 grams costs 2625 yen. Which is the better deal?

14. Solve the following problems (don’t expect whole number answers always!)a. t/5 = 8/7 b. 12/7 = m/43 c. b/10 = 9/6d. 35/22 = 25/y c. 4.8/3 = r/5 d. m/5.8 = 24/6.5