To organise a long calculation, split it into labelled stages, finish each stage on its own line, and only then combine the results. Brackets and powers come first, then multiplication and division, then addition and subtraction.
This skill belongs to non-calculator strategy and uses the fraction moves from choosing an efficient fraction method.
How do you lay out a long question?
- Read the whole question and find the operations inside each bracket.
- Label stages A, B, C. Each stage is one bracket or one operation.
- Solve each stage separately and write its value clearly.
- Combine the stage results in a final line, in the right order.
- Check the size of the final answer with a quick estimate.
Labels cost five seconds each. They also make it easy to find one slip among many correct lines.
Worked example
Work out (2/3 + 1/4) ÷ (5/6 − 1/3), giving the answer as a mixed number.
Stage A, first bracket: 2/3 + 1/4. The lowest common denominator is 12. So 8/12 + 3/12 = 11/12.
Stage B, second bracket: 5/6 − 1/3. The common denominator is 6, and 1/3 = 2/6. So 5/6 − 2/6 = 3/6 = 1/2.
Stage C, combine: 11/12 ÷ 1/2 = 11/12 × 2/1. Cancel 2 with 12 to get 1 and 6. This gives 11/6.
Stage D, convert: 11/6 = 1 5/6.
Check: 2/3 + 1/4 ≈ 0.667 + 0.25 = 0.917, and 5/6 − 1/3 = 0.5. Then 0.917 ÷ 0.5 = 1.833, which matches 1 5/6.
The mistake to watch for
A common error is to add fractions by adding the tops and the bottoms.
Mistaken working: 2/3 + 1/4 = 3/7
The numerators were added (2 + 1) and the denominators were added (3 + 4).
The result 3/7 is about 0.43, which is smaller than 2/3 alone. Adding a positive number cannot make the total smaller, so the answer is impossible. The correct approach is a common denominator: 8/12 + 3/12 = 11/12.
Check yourself
Try these without a calculator, then open each answer.
1. Work out (5/8 − 1/4) × 4/3.
Show answer
Stage A: 5/8 − 2/8 = 3/8. Stage B: 3/8 × 4/3. Cancel 3 with 3 and 4 with 8 to get 1/2. The answer is 1/2.
2. Work out 3/5 + 2/3 × 3/4.
Show answer
Multiplication comes first: 2/3 × 3/4 = 6/12 = 1/2. Then 3/5 + 1/2 = 6/10 + 5/10 = 11/10, which is 1 1/10.
3. A shirt costs RM60. The price is cut by 25%, and the new price is then cut by a further 10%. What is the final price?
Show answer
Stage A: 60 × 0.75 = RM45. Stage B: 45 × 0.9 = RM40.50. The second cut applies to RM45, not RM60.
Where this leads next
The next lesson compares two ways of doing the same calculation: compare two valid mental strategies. When you are ready, try the non-calculator strategy practice set. The percentage-base explorer shows each stage of chained percentage changes, and the non-calculator working trainer does the same for fraction steps.
A teacher who sees how you actually lay out a page can often spot a layout habit that causes repeated slips. That is part of what we look at in online one-to-one Mathematics tuition.