Maths olympiad question · P5–P6★★★★ Expert
Clever sums: olympiad question 11
An expert question on clever sums for P5–P6, with a step-by-step solution, diagrams and the answer. The first few questions of a competition paper are often clever sums, and the Hua Xia Cup has them in every year from P1 to P6.
The question
Work this out the clever way.
18.75 × 1.76 − 375 × 0.297 + 468.75 × 0.3404 − 37.5 × 1.525 = ?
What is the answer?
Show the hints (3)
- Hint 1: Each term's first number is related to 18.75. How many times 18.75 (or what fraction of it) is 375?
- Hint 2: In a product, multiplying one number and dividing the other by the same amount leaves it unchanged. Rewrite every term as 18.75 × something.
- Hint 3: As fractions, every term is 1875 × □ ÷ 10000. What do all the □s come to together?
Worked solution
Have a go first, then read the solution step by step.
1.Write the decimals as fractions. First term: 1875/100 × 176/100 = 1875 × 176 ÷ 10000. - 2.Term 2: 375 × 297/1000; the first number is 20 times 1875/100, so the second is 594/100 divided by 20: the product = 1875 × 594 ÷ 10000.
- 3.Term 3: 46875/100 × 3404/10000; the first number is 25 times 1875/100, so the second is 851/100 divided by 25: the product = 1875 × 851 ÷ 10000.
- 4.Term 4: 375/10 × 1525/1000; the first number is 2 times 1875/100, so the second is 305/100 divided by 2: the product = 1875 × 305 ÷ 10000.
- 5.Take out 1875 ÷ 10000: the whole = 1875 × (176 − 594 + 851 − 305) ÷ 10000 = 1875 × 128 ÷ 10000 = 24.
- ⚠️Common mistake: multiplying each term out as decimals and misplacing a decimal point; or, when moving a factor, multiplying both numbers, which changes the product.
Answer: 24
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