Instructions
Read each question carefully. For the first section, choose the best answer or fill in the blank. For the second section, show your work and write your answers clearly. Good luck!
Part 1: Objective Questions (20 Questions)
Complete the following questions about equivalent ratios and direct proportion.
- Find the missing number to make the ratios equivalent: 2:5 = 4:___
- Which of the following ratios is equivalent to 3:4?
- a) 6:10
- b) 9:12
- c) 12:15
- Write the ratio 16:24 in its simplest form.
- True or False: The ratios 1:3 and 4:12 are equivalent.
- Find the missing number: ___:7 = 15:21
- The ratio of red marbles to blue marbles is 4:9. This is equivalent to 16:___
- If 3 pens cost $6, how much do 5 pens cost?
- Simplify the ratio 50:100 to its simplest form.
- A machine prints 50 pages in 2 minutes. How many pages can it print in 5 minutes?
- True or False: As the number of hours you work increases, the amount of money you earn also increases. This is an example of direct proportion.
- Which pair of ratios is NOT equivalent?
- a) 2:3 and 8:12
- b) 1:5 and 3:15
- c) 4:7 and 12:20
- If a car travels 120 km in 2 hours at a constant speed, how far will it travel in 3 hours?
- A recipe for 4 people requires 200g of flour. How much flour is needed for 6 people?
- The cost of notebooks is directly proportional to the number of notebooks. If 4 notebooks cost $8, what is the cost of 1 notebook?
- Find the missing number: 10:3 = ___:9
- If 1 kg of sugar costs $2.50, the cost of 4 kg of sugar is $_____.
- True or False: As the speed of a car increases, the time it takes to travel a fixed distance decreases. This is an example of direct proportion.
- The ratio of juice concentrate to water is 1:4. If you use 250 ml of concentrate, how much water do you need?
- A tap fills a 20-litre bucket in 4 minutes. How much water will it fill in 6 minutes?
- To make a ratio equivalent to another, you must _______ or _______ both parts of the ratio by the same non-zero number. (Fill in the blanks with "multiply" or "divide").
Part 2: Subjective Questions (10 Questions)
Read the following word problems. Write down your steps and the final answer.
- A pancake recipe calls for 1 cup of flour for every 2 eggs. If you want to make a larger batch using 8 eggs, how many cups of flour will you need? Show your work.
- Write three different ratios that are equivalent to 4:5.
- A map has a scale where 1 cm represents 20 km in real life. If the distance between two cities on the map is 7.5 cm, what is the actual distance between them in kilometers?
- In your own words, what does it mean for two quantities to be in direct proportion? Give one real-life example.
- A painter is mixing green paint. The ratio of blue paint to yellow paint is 3:7. If she uses 12 liters of blue paint, how much yellow paint does she need to use?
- Sam earns $48 for working 4 hours at a cafe. How much will he earn if he works for 7 hours, assuming the pay rate is constant?
- A cyclist travels 30 km in 2 hours. At this constant speed, how long will it take the cyclist to travel 75 km?
- The ratio of fiction books to non-fiction books in a school library is 9:4. If there are 360 non-fiction books, how many fiction books are there?
- Complete the table below, assuming the cost of fabric is in direct proportion to its length. Then, find the cost of 1 meter of fabric.
Length (meters) 2 5 __ 12 Cost ($) 10 __ 40 __ - A school is planting trees for an environmental project. For every 3 pine trees they plant, they plant 4 oak trees. If they plant a total of 42 trees, how many are pine trees and how many are oak trees?
Answer Key
Part 1: Objective Questions
- 10
- b) 9:12
- 2:3
- True
- 5
- 36
- $10
- 1:2
- 125 pages
- True
- c) 4:7 and 12:20
- 180 km
- 300g
- $2
- 30
- $10.00
- False (This is inverse proportion)
- 1000 ml or 1 litre
- 30 litres
- multiply, divide
Part 2: Subjective Questions
- Answer: 4 cups of flour.
Work: The ratio is 1 flour : 2 eggs. To find out how much flour for 8 eggs, you can set up an equivalent ratio: 1/2 = x/8. Since 2 x 4 = 8, you must also multiply 1 by 4. So, 1 x 4 = 4 cups of flour. - Answer: Any three of the following or other correct equivalents: 8:10, 12:15, 16:20, 40:50, etc. (The ratio is maintained by multiplying both numbers by the same value).
- Answer: 150 km.
Work: The ratio is 1 cm : 20 km. For 7.5 cm, you multiply 7.5 by 20. (7.5 x 20 = 150). - Answer: (Example Answer) Direct proportion means that as one quantity increases, the other quantity increases at the same rate. If one quantity doubles, the other one also doubles.
Example: The more gasoline you buy (quantity 1), the more money you have to pay (quantity 2). - Answer: 28 liters of yellow paint.
Work: The ratio is 3 blue : 7 yellow. To get from 3 blue to 12 blue, you multiply by 4. So, you must also multiply the yellow paint by 4. (7 x 4 = 28). - Answer: $84.
Work: First find the hourly rate: $48 / 4 hours = $12 per hour. Then multiply by the new hours: $12 x 7 hours = $84. - Answer: 5 hours.
Work: First find the speed: 30 km / 2 hours = 15 km per hour. Then find the time for 75 km: 75 km / 15 km/h = 5 hours. - Answer: 810 fiction books.
Work: The ratio is 9 fiction : 4 non-fiction. Set up the proportion: 9/4 = x/360. To get from 4 to 360, you multiply by 90 (360 / 4 = 90). So, multiply 9 by 90. (9 x 90 = 810). - Answer:
Cost of 1 meter: $10 / 2 meters = $5 per meter.Length (meters) 2 5 8 12 Cost ($) 10 25 40 60 - Answer: 18 pine trees and 24 oak trees.
Work: The ratio is 3 pine + 4 oak = 7 parts in total. Divide the total trees by the total parts: 42 / 7 = 6 trees per part.
Pine trees: 3 parts x 6 = 18.
Oak trees: 4 parts x 6 = 24.
(Check: 18 + 24 = 42).