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Fractions · fraction of the remainder
P6 · Fractions · PSLE Maths
Question
Mei Ling had some money at a school fair. She first spent 1/4 of her money on a class T-shirt. She then spent 2/5 of the remaining money on a storybook and pens. She had $54 left. How much money did Mei Ling have at first?
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Hint
First divide the whole into 4 parts. Then divide the remaining 3/4 into 5 equal parts. How many of these parts are left at the end?
Show the answer and step-by-step explanation
Answer: Mei Ling at first 120 $
- Draw the whole — Look at the first spending: Mei Ling spent 1/4 of all her money. So divide the whole into 4 equal parts. 1 part was spent and 3 parts were left.
- Split the remainder — The second spending is 2/5 of the remaining money. Be careful: we do not divide the whole into 5 parts. We divide the 3/4 left into 5 equal parts.
- Mark the final amount — After spending 2/5 the second time, 3/5 of the remainder was left. These 3 parts on the model are the final $54.
- Find 1 small unit — Look at the small units. The 3 large parts left after the first spending each have 5 small units, so the final 3 parts have 9 small units altogether. 9 small units = $54, so 1 small unit = $6.
- Find the original amount — The whole bar has 20 small units. Each small unit is $6, so the original amount is 20 × $6 = $120.
- Check — Check: 1/4 of $120 is $30, leaving $90. 2/5 of $90 is $36, leaving $54. This matches the question. 📌 Key idea: draw the whole first, then split the remainder again. Use the final amount left to work backwards to 1 small unit, then find the whole.
Method: For a fraction of the remainder, first draw the amount left after the first step, then divide this remainder again. Use the final amount left to find 1 small unit, then find the whole.
Practice: 3 similar questions
- Ali took some money to a school carnival. He first spent 1/3 of his money on games. He then spent 1/4 of the remaining money on snacks. He had $60 left. How much money did Ali have at first?
Answer
120 $ — After the first spending, 1 − 1/3 = 2/3 was left. He spent 1/4 of the remainder, so 3/4 of the remainder was left. The final amount left was 2/3 × 3/4 = 1/2 of the whole. 1/2 = $60, so the whole amount = $60 × 2 = $120.
- Raju had some game cards. He first gave 2/7 of all his cards to his cousin. He then gave 3/5 of the remaining cards to his friends. He had 24 cards left. How many cards did Raju have at first?
Answer
84 cards — After the first step, 1 − 2/7 = 5/7 was left. He gave away 3/5 of the remainder, so 2/5 of the remainder was left. The final amount left was 5/7 × 2/5 = 2/7 of all the cards. 2/7 = 24 cards, so 1/7 = 12 cards and the whole = 7 × 12 = 84 cards.
- Siti had some money. She first spent 2/5 of her money on a school bag. She then spent 1/3 of the remaining money on a water bottle. In the end, she had $28 more than the amount spent on the water bottle. How much money did Siti have at first?
Answer
140 $ — After the first spending, 1 − 2/5 = 3/5 was left. The water bottle cost 1/3 of the remainder, so it was 3/5 × 1/3 = 1/5 of the whole. The final amount left was 2/3 of the remainder: 3/5 × 2/3 = 2/5 of the whole. The final amount was more than the water bottle cost by 2/5 − 1/5 = 1/5 of the whole. 1/5 = $28, so the whole amount = $28 × 5 = $140.
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