Fractions Practice 2 — P5 Mathematics

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Instructions: This worksheet has 10 challenging word problems. Answer all questions. Show all working. Express your answers as fractions in their simplest form or as mixed numbers where appropriate. Total: 10 questions.

Key Concepts Covered

Fraction of remaining (two-stage problems)
Equal amount removed from two quantities (constant difference)
Mixed fraction and whole number word problems
Money, measurement, and time contexts
Multi-step reasoning with bar models or unit method

Practice

Challenging Word Problems

~25 min

Show all your working. Express answers as fractions in their simplest form or as mixed numbers.

A baker baked a batch of muffins. He sold 3/5 of the muffins in the morning, 2/3 of the remaining muffins in the afternoon, and had 24 muffins left.

(a) What fraction of the total muffins were sold in the afternoon?
(b) How many muffins did the baker bake at first?

Jar A contained 3kg 200g of water. Jar B contained 7.4kg of water. Sarah poured out an equal amount of water from each jar. Then, the amount of water in Jar B became 5 times that of Jar A. How much water did Sarah pour out from each jar? Give your answer in kg.

Mei Ling had a piece of string. She used 170cm of it to tie a parcel. She then used 4/7 of the remaining string to make a bracelet. At the end, she discovered she had 1/8 of the original string left. How long was the string at first?

A bookstore received a shipment of notebooks. It sold 2/5 of them on the first day and 3/4 of the remaining notebooks on the second day, leaving 60 notebooks unsold.

(a) What fraction of the total shipment was sold on the second day?
(b) How many notebooks were in the original shipment?

Daniel had $96 in his wallet and Ethan had $276 in his. Both of them spent an equal amount on a pair of sneakers. After that, Ethan had 4 times as much money left as Daniel. How much did the sneakers cost?

Ryan spent $65 of his monthly allowance on a video game. He then used 3/5 of the remaining money to buy comics. He had 1/9 of his original monthly allowance left. How much was Ryan's monthly allowance at first?

A shopkeeper had a stock of pens. He sold 4/9 of the pens on Monday and 2/5 of the remaining pens on Tuesday. If he had 180 pens left, how many pens did he have at first?

A tank contained some water. John poured out 3/4 of the water and then added 2 litres back into the tank. He then used 1/3 of the remaining water to water his plants. If there were 5 litres left in the tank, how much water was in the tank at first?

Box P contained 1kg 500g of rice. Box Q contained 4.2kg of rice. An equal amount of rice was removed from each box. After that, the amount of rice in Box Q became 3 times that of Box P. How much rice was removed from each box? Give your answer in kg.

A fruit vendor had a crate of apples. He sold 5/8 of the apples in the morning. In the afternoon, he sold 1/3 of the remaining apples and had 40 apples left.

(a) What fraction of the total apples were sold in the afternoon?
(b) How many apples were in the crate at first?
(c) If the apples were sold at $1.20 each, how much money did the vendor collect from all the apples sold?

Answer Key

Q1.

(a) Remaining after morning: 1 - 3/5 = 2/5. Afternoon sales: 2/3 × 2/5 = 4/15
(b) Fraction left: 2/5 - 4/15 = 6/15 - 4/15 = 2/15. Since 2/15 = 24 muffins, 1/15 = 12. Total: 15 × 12 = 180 muffins

Q2.

Jar A: 3.2 kg, Jar B: 7.4 kg. Difference: 7.4 - 3.2 = 4.2 kg (constant)
After pouring: B = 5A, so difference = 5u - 1u = 4u = 4.2 kg
1u = 1.05 kg (amount left in Jar A)
Poured out: 3.2 - 1.05 = 2.15 kg

Q3.

After using 4/7 of remaining, 3/7 of remaining is left. This equals 1/8 of original.
Let total = T cm. Remainder after first use: T - 170
3/7 × (T - 170) = T/8 → 24(T - 170) = 7T → 24T - 4080 = 7T → 17T = 4080
T = 240 cm

Q4.

(a) Remaining after day 1: 1 - 2/5 = 3/5. Day 2 sales: 3/4 × 3/5 = 9/20
(b) Fraction left: 3/5 - 9/20 = 12/20 - 9/20 = 3/20. Since 3/20 = 60, 1/20 = 20. Total: 20 × 20 = 400 notebooks

Q5.

Daniel: $96, Ethan: $276. Difference: $276 - $96 = $180 (constant)
After spending: E = 4D, so difference = 4u - 1u = 3u = $180
1u = $60 (Daniel's remaining amount)
Sneakers cost: $96 - $60 = $36

Q6.

After spending $65, remainder = T - 65. Used 3/5 of (T-65), so left = 2/5 × (T-65) = T/9
2(T-65)/5 = T/9 → 18(T-65) = 5T → 18T - 1170 = 5T → 13T = 1170
T = $90

Q7.

Remaining after Monday: 1 - 4/9 = 5/9. Tuesday sales: 2/5 × 5/9 = 2/9
Fraction left: 5/9 - 2/9 = 3/9 = 1/3. Since 1/3 = 180, total = 540 pens

Q8.

Let original = T litres. After pouring out 3/4: T/4 left. Add 2L: T/4 + 2
Used 1/3 of (T/4 + 2), so left = 2/3 × (T/4 + 2) = 5
T/4 + 2 = 7.5 → T/4 = 5.5 → T = 22 litres

Q9.

Box P: 1.5 kg, Box Q: 4.2 kg. Difference: 4.2 - 1.5 = 2.7 kg (constant)
After removing: Q = 3P, so difference = 3u - 1u = 2u = 2.7 kg
1u = 1.35 kg (amount in Box P after removal)
Removed: 1.5 - 1.35 = 0.15 kg

Q10.

(a) Remaining after morning: 1 - 5/8 = 3/8. Afternoon sales: 1/3 × 3/8 = 1/8
(b) Fraction left: 3/8 - 1/8 = 2/8 = 1/4. Since 1/4 = 40, total = 160 apples
(c) Total sold: 5/8 × 160 + 1/8 × 160 = 100 + 20 = 120. Revenue: 120 × $1.20 = $144