Fractions, Decimals and Percentages Challenge

Name:

Date:

Part 1: Apply and Convert

Instructions: Read each problem carefully. Show every step, label your answers and give exact answers where possible. Use a calculator only when your tutor allows it. Round money to the nearest cent and other answers to the nearest tenth when requested.

Success criteria: I can convert between fractions, decimals and percentages; choose suitable operations; explain my reasoning; and check whether my answer is realistic.

Support strategy: Underline the important information, draw a simple diagram if helpful, and write a sentence explaining what each calculation represents.

1. Mia has $80. She spends 3/8 of it on a book and saves 20% of what remains. How much money is left? Give the amount left as a fraction, decimal and percentage of the original $80.

2. A recipe uses 2 1/4 cups of flour to make 6 muffins. Sam wants to make 10 muffins. How much flour is needed? Give your answer as a mixed number and a decimal. If each scoop holds 1/4 cup, how many scoops are needed?

3. A 18 km charity route is 5/12 walked and the rest cycled. Of the cycling distance, 2/7 is uphill. Find the total cycling distance and the uphill distance.

4. A jacket costs $120. It is reduced by 15%, then 10% GST is added to the sale price. What is the final price? How much has the customer saved compared with paying the original price before GST?

5. In a class of 28 students, 3/7 travel by bus. Of the students remaining, 25% cycle. The rest walk. How many students walk, and what percentage of the whole class is this? Round the percentage to 1 decimal place.

6. A bag contains 5 red, 3 blue and 2 green counters. Two counters are selected without replacement. What is the probability that they are different colours? Give the answer as a simplified fraction and a percentage to 1 decimal place.

Part 2: Multi-Step Reasoning

7. A bicycle helmet is priced at $240 and is discounted by 0.375 of its price. Convert 0.375 to a fraction and a percentage. Then calculate the discount and the price paid.

8. A school survey has 40 responses. 35% prefer travelling by train, 3/8 prefer the bus and the rest prefer travelling by car. Find the number and percentage for each method. If two car users change to train, what percentage then prefer train?

9. An investment of $600 increases by 12% in one month and then decreases by 12% the next month. What is its final value? Is the final value the same as the starting value? Find the overall percentage change.

10. On a map, 2.5 cm represents 4 km. A cycling route measures 7.75 cm on the map. The cyclist completes 5/8 of the route before resting. Find the real distance of the route and the distance completed before the rest.

11. A phone plan includes 15 GB of data. A student uses 2/5 for streaming and 30% of the remaining data for games. How much data remains? Express the remaining amount as a fraction and percentage of the original allowance.

12. Each week, Noah saves $45. He puts 3/5 into a holiday fund. Of the money left, he spends 20% on gifts and keeps the rest. Over 8 weeks, how much goes into the holiday fund, how much is spent on gifts and how much is kept?

13. A tank holds 240 L and is initially 5/8 full. A gardener uses 30% of the water in the tank and then adds 24 L. What volume is now in the tank? Give this as a fraction and percentage of the tank’s capacity.

14. A student scores 3/4 of 40 marks on the first test. The second test is worth 60 marks. What score is needed on the second test to achieve 75% overall across both tests? What percentage is this of the second test?

Part 3: Extension Challenges and Answer Key

Extension strategy: For advanced learners, solve Questions 15–18 without rounding until the final step. Try to write an equation before calculating and explain why your method works.

15. Extension. Priya invests $250. The investment gains 8%, then a management fee of 2% of the new value is taken. Find the final amount and the overall percentage gain, rounded to 2 decimal places.

16. Extension. A recipe needs 3/4 kg of flour for 12 serves. A chef prepares 30 serves and expects 10% of the flour bought to be spilled. If the chef buys 2 kg, is there enough usable flour? Find the exact shortfall or surplus.

17. Extension. At a raffle, 40% of 60 tickets are online. Of the remaining tickets, 2/3 belong to adults and the rest belong to children. If two tickets are selected without replacement, what is the probability that both belong to children? Give a simplified fraction and a percentage to 1 decimal place.

18. Extension. A tablet’s marked price is reduced by 20%, then 10% GST is added. A $15 voucher is used after GST. The final amount paid is $249. What was the marked price? What percentage of the marked price was saved in total?

Answer Key

1. Spent: 80 × 3/8 = $30. Remaining: $50. Saved: 20% of $50 = $10. Left: $40 = 1/2 = 0.5 = 50%.

2. 2 1/4 × 10/6 = 15/4 = 3 3/4 cups = 3.75 cups. Scoops: 3.75 ÷ 0.25 = 15 scoops.

3. Cycled: 18 × 7/12 = 10.5 km. Uphill: 10.5 × 2/7 = 3.0 km.

4. Sale price: 120 × 0.85 = $102. GST: 102 × 0.10 = $10.20. Final price: $112.20. Saving: 120 − 112.20 = $7.80.

5. Bus: 28 × 3/7 = 12. Remaining: 16. Cycling: 16 × 0.25 = 4. Walking: 12 students. Percentage: 12/28 × 100 = 42.9%.

6. Total pairs: 45. Same-colour pairs: 10 + 3 + 1 = 14. Different-colour pairs: 31. Probability: 31/45 = 68.9%.

7. 0.375 = 3/8 = 37.5%. Discount: 240 × 0.375 = $90. Price paid: $150.

8. Train: 14, bus: 15, car: 11. Car percentage: 11/40 = 27.5%. After two change: train 16/40 = 40%.

9. 600 × 1.12 × 0.88 = $591.36. Overall change: $8.64 decrease, which is 1.44% decrease.

10. 7.75 ÷ 2.5 × 4 = 12.4 km. Completed: 12.4 × 5/8 = 7.75 km.

11. Streaming: 15 × 2/5 = 6 GB. Remaining: 9 GB. Games: 9 × 0.3 = 2.7 GB. Left: 6.3 GB = 21/50 = 42%.

12. Holiday: 45 × 3/5 × 8 = $216. Remaining each week: $18. Gifts: 18 × 0.2 × 8 = $28.80. Kept: 18 × 0.8 × 8 = $115.20.

13. Initial: 240 × 5/8 = 150 L. Used: 150 × 0.3 = 45 L. Final: 150 − 45 + 24 = 129 L. Fraction: 129/240 = 43/80. Percentage: 53.75%.

14. First score: 40 × 3/4 = 30. Target: 100 × 0.75 = 75. Second score: 75 − 30 = 45 marks. Percentage: 45/60 = 75%.

15. After gain: 250 × 1.08 = $270. Fee: 270 × 0.02 = $5.40. Final: $264.60. Gain: $14.60 ÷ $250 × 100 = 5.84%.

16. Flour needed: 3/4 × 30/12 = 15/8 kg = 1.875 kg. Usable flour: 2 × 0.9 = 1.8 kg. Shortfall: 1.875 − 1.8 = 0.075 kg, or 75 g.

17. Online: 24. Remaining: 36. Adult: 24, child: 12. Probability: 12/60 × 11/59 = 132/3540 = 11/295 ≈ 3.7%.

18. Final equation: 0.8 × 1.1 × price − 15 = 249. Price = 264 ÷ 0.88 = $300. Total saving: $300 − $249 = $51. Percentage: 51/300 × 100 = 17%.

Success criteria check: I showed my working, converted accurately, rounded only when instructed, used units and checked that my final answers were reasonable.