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Fractions · equal amount left
P6 · Fractions · PSLE Maths
Question
Ali and Siti had $465 altogether. Ali spent 3/8 of his money and Siti spent 1/3 of her money. After that, they had the same amount of money left. How much money did Ali and Siti have at first?
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Hint
First find the fraction left for each person, then draw the two equal left amounts with the same length.
Show the answer and step-by-step explanation
Answer: Ali at first 240 $; Siti at first 225 $
- Find left — Ali spent 3/8, so he had 5/8 left. Siti spent 1/3, so she had 2/3 left. The question says these two amounts left are equal.
- Use same units — Ali's 5 parts left are equal to Siti's 2 parts left. Use 10 small units as a common number, so the two left parts have the same length.
- Draw model — Now draw the model using small units: Ali had 8 eighths at first, and each eighth is 2 small units, so he had 16 small units. Siti had 3 thirds at first, and each third is 5 small units, so she had 15 small units.
- Total units — Both left parts are 10 small units, so they are equal. At first, there were Ali's 16 small units and Siti's 15 small units, which make 31 small units altogether.
- Value of 1 unit — The question says they had $465 altogether at first. So 31 small units = $465, and 1 small unit = $15.
- Find amounts — Ali had 16 small units at first: 16 × $15 = $240. Siti had 15 small units at first: 15 × $15 = $225. Check: Ali had $150 left, and Siti also had $150 left. 📌 Key idea: when the amounts left are equal, make the left fractions the same number of small units first, then use the total to find 1 unit.
Method: Find the fraction left first. Since the amounts left are equal, use common units for the equal left parts, then find the total number of units at first.
Practice: 3 similar questions
- Raju and Siti had $340 altogether. Raju spent 2/7 of his money and Siti spent 1/2 of her money. After that, they had the same amount of money left. How much money did Raju and Siti have at first?
Answer
140 $, 200 $ — Raju had 1 − 2/7 = 5/7 left; Siti had 1 − 1/2 = 1/2 left. Make the equal left parts 5 small units each. Raju had 7 small units at first; Siti's 1/2 is 5 small units, so she had 10 small units at first. Total units: 7 + 10 = 17 small units. 1 small unit = 340 ÷ 17 = $20. Raju had 7 × $20 = $140 at first; Siti had 10 × $20 = $200 at first.
- Ali and Mei Ling had $484 altogether at the school carnival. Ali spent 3/8 of his money and Mei Ling spent 1/4 of her money. After that, they had the same amount of money left. How much money did Ali and Mei Ling have at first?
Answer
264 $, 220 $ — Ali had 5/8 left and Mei Ling had 3/4 left. Use 15 small units for the equal left parts: Ali's 5 parts = 15 small units, so he had 8 × 3 = 24 small units at first. Mei Ling's 3 parts = 15 small units, so she had 4 × 5 = 20 small units at first. Total units: 24 + 20 = 44 small units. 1 small unit = 484 ÷ 44 = $11. Ali had 24 × $11 = $264 at first; Mei Ling had 20 × $11 = $220 at first.
- Raju and Mei Ling had $679 altogether. Raju spent 5/11 of his money and Mei Ling spent 2/7 of her money. After that, they had the same amount of money left. How much money did Raju and Mei Ling have at first?
Answer
385 $, 294 $ — Raju had 1 − 5/11 = 6/11 left; Mei Ling had 1 − 2/7 = 5/7 left. Make the equal left parts 30 small units. Raju's 6 parts = 30 small units, so 1/11 = 5 small units and he had 11 × 5 = 55 small units at first. Mei Ling's 5 parts = 30 small units, so 1/7 = 6 small units and she had 7 × 6 = 42 small units at first. Total units: 55 + 42 = 97 small units. 1 small unit = 679 ÷ 97 = $7. Raju had 55 × $7 = $385 at first; Mei Ling had 42 × $7 = $294 at first.
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