Proportional Reasoning Practice

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Date:

📊 Part 1: Converting and Comparing

1. Convert each value to a decimal and a percentage. Show your working.

a) 5/8 = _______ = _______%

b) 7/12 = _______ = _______%

c) 1 3/5 = _______ = _______%

2. Circle the largest value in each group. Convert the values if necessary before comparing them.

Group A: 0.72 7/10 71% 3/4

Group B: 0.416 5/12 41% 0.42

3. Find the missing values in these equivalent ratios. Give each answer in its simplest form.

a) 3 : 8 = 15 : _____

b) 18 : 30 = _____ : 25

c) 4 : 7 = 2.4 : _____

d) 2.5 : 6 = _____ : 18

4. In a class, 3/8 of the students are boys. Of the girls, 20% are absent. If there are 96 students in the class, how many girls are present?

🛒 Part 2: Real-Life Shopping Problems

5. At the supermarket, Sarah compares these deals. Deal A has a 10% discount, while Deal B has a $1.50 coupon. Which deal gives the lower price per bottle?

Deal A: 3 bottles of juice for $6.60, with 10% off

Deal B: 5 bottles of juice for $9.50, with a $1.50 coupon

6. A jacket costs $120. It is reduced by 25% in a sale, and then an additional 10% is taken off the reduced price. What is the final price, and what percentage of the original price does the customer pay?

7. Tom buys 2.5 kg of apples at $4.80 per kilogram. He uses a voucher for 15% off his total purchase and pays with $20. How much change should he receive?

8. A recipe serves 4 people and uses 300 g of flour and 180 ml of milk. Mia wants to serve 10 people, but 8% of the flour is lost when it is measured. How much flour should she measure out, and how much milk will she need?

🎯 Part 3: Multi-Step Problem Solving

9. In a survey of 240 students, 5/8 like pizza. Of the remaining students, 45% like burgers. How many students like neither pizza nor burgers?

10. A car travels 240 kilometres in 3 hours. It continues at this rate for 2.5 hours, then travels 20% farther during the next hour because of a faster route. How far does it travel altogether?

11. A school spends 35% of its budget on technology and 2/5 of the remaining budget on sports equipment. If the total budget is $48,000, how much money is left for all other expenses? Show each step of your reasoning.

12. Explain how you would compare 0.7, 2/3, 65%, and 11/16 to find the largest value. Convert all four values to the same form and justify your answer.