Solving Proportions

Show your work for each problem.

1.
What method is used to solve proportions by multiplying diagonally?
1. a)Factoring
2. b)Long division
3. c)Cross multiplication
4. d)Square root
Answer: Cross multiplication
Cross multiplication means multiplying diagonally across the equal sign: if , then .
2.
Solve for :
Answer: 6
Cross multiply: , so . Divide both sides by 5: .
3.
Which equation correctly shows cross multiplication for ?
1. a)
2. b)
3. c)
4. d)
Answer:
Cross multiply: . This gives , so .
4.
Solve the proportion:
Answer: 15
1. Write the cross multiplication equation: 60
2. Now you have . Divide both sides by 4. What is ? 15
5.
Solve for :
Answer: 6
Cross multiply: , so . Divide by 4: .
6.
If 5 apples cost 3 euros, how much do 15 apples cost?
Answer: 9
1. Set up the proportion. If apples are on top and cost on bottom, what goes in the second fraction's numerator? 15
2. Now cross multiply: . What is ? 45
3. Solve . What is ? 9
7.
Solve for :
Answer: 28
Cross multiply: , so . Divide by 2: .
8.
A recipe uses 3 cups of flour for 12 cookies. How many cups are needed for 20 cookies?
1. a)4 cups
2. b)7 cups
3. c)5 cups
4. d)6 cups
Answer: 5 cups
Set up . Cross multiply: , so . Divide: cups.
9.
On a map, 4 cm represents 50 km. If two cities are 10 cm apart on the map, what is the actual distance?
Answer: 125
1. Set up the proportion with cm on top and km on bottom. For the first ratio: . What goes on top of the second ratio? 10
2. Cross multiply: . What is ? 500
3. Solve . What is ? 125
10.
Solve for :
Answer: 21
Cross multiply: , so . Divide by 6: .
11.
What is the scale factor from the first ratio to the second in ?
1. a)5
2. b)3
3. c)4
4. d)2
Answer: 3
The scale factor is 3 because and . Both parts are multiplied by the same number.
12.
A car travels 180 km on 15 liters of fuel. How many liters are needed to travel 300 km?
Answer: 25
1. Set up the proportion with km on top and liters on bottom. What is the first ratio? 180/15
2. Cross multiply: . What is ? 4500
3. Solve . What is ? 25
13.
Solve for :
Answer: 6.25
Cross multiply: , so . Divide by 4: .
14.
A medicine is dosed at 5 mg per 2 kg of body weight. What dose should a 70 kg patient receive?
Answer: 175
1. Set up the proportion: . Cross multiply: 350
2. You have . What is ? 175
15.
A model car is built at a scale of 1:24. If the real car is 4.8 m long, how long is the model in cm?
1. a)24 cm
2. b)12 cm
3. c)48 cm
4. d)20 cm
Answer: 20 cm
4.8 m = 480 cm. Scale 1:24 means the model is of the real size. cm.
16.
Using the scale factor method: If , find .
Answer: 14
1. Find the scale factor: What do you multiply 12 by to get 21? (as a fraction or decimal) 1.75
2. Apply the scale factor to 8: 14