This set mixes the five skills from non-calculator strategy: choosing a fraction method, keeping exact values, estimating, organising working and comparing mental strategies. The questions are in rough order from easier to harder.
Attempt each one on paper with no calculator. Write the working first, then open the answer and compare the method as well as the result.
Questions
Q1. Work out 7/12 + 3/8.
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The lowest common denominator is 24. 7/12 = 14/24 and 3/8 = 9/24. So 14/24 + 9/24 = 23/24.
Check: 0.583 + 0.375 = 0.958, and 23/24 = 0.958.
Q2. Work out 9/10 ÷ 3/5.
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Multiply by the reciprocal: 9/10 × 5/3. Cancel 9 with 3 to get 3 and 1, and cancel 5 with 10 to get 1 and 2. This gives 3/2, which is 1 1/2.
Check: 0.9 ÷ 0.6 = 1.5.
Q3. Work out 14/15 × 5/21, cancelling before you multiply.
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Cancel 14 with 21 (both divide by 7) to get 2 and 3. Cancel 5 with 15 to get 1 and 3. The product is (2 × 1) / (3 × 3) = 2/9.
Check: multiplying straight across gives 70/315, and dividing top and bottom by 35 gives 2/9.
Q4. A sector has radius 9 cm and angle 40°. Find its area in terms of π.
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Area = 40/360 × π × 9². Now 40/360 = 1/9 and 9² = 81. So 1/9 × 81 × π = 9π cm².
Check: a full circle is 81π, and 40° is one ninth of 360°, so the sector is 81π ÷ 9 = 9π.
Q5. A student finds 2/3 of 1200 by using 0.67 × 1200. What answer do they get, and how far is it from the exact answer?
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0.67 × 1200 = 804. The exact answer is 1200 ÷ 3 × 2 = 800. The rounded decimal gives an answer that is 4 too big, and the gap grows with bigger amounts.
Q6. Estimate 5.03 × 19.8. Which of 9.96, 99.6 or 996 is the correct value, and why?
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5.03 ≈ 5 and 19.8 ≈ 20, so the estimate is 5 × 20 = 100. Only 99.6 is close to 100. The others are ten times too small and ten times too big.
Q7. A student says 41.2 ÷ 0.79 = 5.2. Use an estimate to decide whether this is possible.
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41.2 ≈ 40 and 0.79 ≈ 0.8, so the estimate is 40 ÷ 0.8 = 50. The answer 5.2 is ten times too small, so it is impossible. The correct value is about 52.15, which the estimate of 50 supports.
Q8. Work out (3/4 + 1/6) ÷ (2 − 1/3), laying out your working in stages.
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Stage A: 3/4 + 1/6 = 9/12 + 2/12 = 11/12.
Stage B: 2 − 1/3 = 6/3 − 1/3 = 5/3.
Stage C: 11/12 ÷ 5/3 = 11/12 × 3/5. Cancel 3 with 12 to get 1 and 4. This gives 11/20.
Answer: 11/20. Check: 0.9167 ÷ 1.6667 = 0.55, and 11/20 = 0.55.
Q9. RM200 is increased by 20%, and the new amount is then decreased by 20%. What is the final amount?
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Stage A: 200 × 1.2 = RM240. Stage B: 240 × 0.8 = RM192.
The second change is applied to RM240, not RM200, so the final amount is lower than the start. Try the percentage-base explorer to see this with other numbers.
Q10. Work out 97 × 12 by two different methods and confirm they agree.
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Method 1: 100 × 12 = 1200, then subtract 3 lots of 12. 1200 − 36 = 1164.
Method 2: 97 × 10 = 970 and 97 × 2 = 194. Then 970 + 194 = 1164.
Both methods give 1164.
Q11. Work out 2 1/2 × (4/5 − 3/10). Give the answer as a mixed number.
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Stage A: 4/5 − 3/10 = 8/10 − 3/10 = 5/10 = 1/2.
Stage B: 2 1/2 = 5/2, so 5/2 × 1/2 = 5/4.
Answer: 1 1/4. Check: 2.5 × 0.5 = 1.25.
If you got these wrong
Use this table to send each error to the lesson that fixes it.
| Type of error | Questions | Go to |
|---|---|---|
| Wrong fraction method, or long route | Q1, Q2, Q3 | choose an efficient fraction method |
| Rounded too early, or lost π | Q4, Q5 | use exact values instead of premature decimals |
| Answer the wrong size | Q6, Q7 | estimate to reject an impossible answer |
| Lost track in a long question | Q8, Q9, Q11 | organise working for a multi-operation task |
| Only one method, no check | Q10 | compare two valid mental strategies |
Keep a short note of each error type in the mistake log and retest queue and retry a fresh question a few days later. The non-calculator working trainer gives extra step-by-step tasks.
If the same error returns after you have reread the lesson, it is usually a habit rather than a gap in knowledge. A teacher who reads your working one-to-one can find it quickly in online one-to-one Mathematics tuition.