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Multi-Step Word Problems — Strategies and Examples

By MathPal Editorial Team·Published

Grade: 6-7 | Topic: Arithmetic

What You Will Learn​

Multi-step word problems are the bridge between pure arithmetic and real-world reasoning. This guide teaches you a clear strategy for identifying sub-questions hidden inside a longer problem and solving each one systematically — so you never get lost partway through.

Theory​

The 4-step strategy​

Step 1 — Read: Read the whole problem once without calculating. Identify:

  • What is given (the facts)?
  • What is asked (the final question)?

Step 2 — Plan: Identify the sub-questions you need to answer before you can reach the final answer. Write these down as mini-steps.

Step 3 — Solve: Work through each sub-question in order. Show each calculation clearly. Keep track of units.

Step 4 — Check: Does the answer make sense? Re-read the question and verify your answer addresses exactly what was asked.

Key word signals​

Key wordLikely operation
total, sum, altogether, combinedAddition
difference, left, remaining, fewerSubtraction
each, per, times, productMultiplication
shared equally, split, per person, dividedDivision
fraction of, percentage ofMultiplication by a fraction or decimal
how much more/lessSubtraction, then compare

Handling units​

Always track units (dollars, metres, kg, hours) throughout your working. If you multiply metres by metres you get square metres — check this matches what the question asks for.

Worked Examples​

Example 1 — Shopping problem​

Lena buys 3 notebooks for $2.50 each and 2 pens for $1.80 each. She pays with a $20 note. How much change does she receive?

Sub-question 1: Cost of notebooks = 3×2.50=7.503 \times 2.50 = 7.50

Sub-question 2: Cost of pens = 2×1.80=3.602 \times 1.80 = 3.60

Sub-question 3: Total cost = 7.50+3.60=11.107.50 + 3.60 = 11.10

Sub-question 4: Change = 20.00−11.10=8.9020.00 - 11.10 = 8.90

Answer: Lena receives $8.90 change.

Example 2 — Distance and time​

A car travels 180 km in 2 hours, then travels another 120 km in 1.5 hours. What is the average speed for the whole journey?

Sub-question 1: Total distance = 180+120=300180 + 120 = 300 km

Sub-question 2: Total time = 2+1.5=3.52 + 1.5 = 3.5 hours

Sub-question 3: Average speed = 3003.5≈85.7\dfrac{300}{3.5} \approx 85.7 km/h

Answer: The average speed is approximately 85.7 km/h.

Example 3 — Fractions and whole numbers​

A bag of rice weighs 5 kg. A family uses 34\dfrac{3}{4} of the bag in a month. How many grams are left?

Sub-question 1: Amount used = 5×34=154=3.755 \times \dfrac{3}{4} = \dfrac{15}{4} = 3.75 kg

Sub-question 2: Amount remaining = 5−3.75=1.255 - 3.75 = 1.25 kg

Sub-question 3: Convert to grams = 1.25×1000=12501.25 \times 1000 = 1250 g

Answer: There are 1,250 g of rice left.

Example 4 — Percentages and money​

A jacket originally costs $80. It is first discounted by 20%, then an 8% sales tax is added. What is the final price?

Sub-question 1: Discount amount = 80×0.20=1680 \times 0.20 = 16

Sub-question 2: Price after discount = 80−16=6480 - 16 = 64

Sub-question 3: Tax amount = 64×0.08=5.1264 \times 0.08 = 5.12

Sub-question 4: Final price = 64+5.12=69.1264 + 5.12 = 69.12

Answer: The final price is $69.12.

Common Mistakes​

Mistake 1 — Answering a sub-question instead of the final question​

❌ In Example 1, stopping after calculating the total cost ($11.10) instead of finding the change.

✅ Always re-read the question after each step. The last step must match exactly what was asked.

Mistake 2 — Applying the percentage to the wrong amount​

❌ In Example 4, calculating 8% tax on $80 (the original price) rather than on the discounted price of $64.

✅ Operations must be applied in the correct order. Discount first, then tax on the reduced price.

Mistake 3 — Mixing units​

❌ Adding 1.25 kg + 500 g = 1.75 (wrong units).

✅ Convert all quantities to the same unit before combining: 1.25 kg = 1250 g, then 1250 + 500 = 1750 g.

Practice Problems​

Problem 1: A cinema sells adult tickets for $14 and child tickets for $9. A family buys 2 adult and 3 child tickets. They have a voucher worth $10. How much do they pay?

Show Answer

Adults: 2×14=2 \times 14 = $28. Children: 3×9=3 \times 9 = $27. Total before voucher: $55. After voucher: $55 - $10 = $45.

Problem 2: A factory produces 450 items per hour. It runs 8 hours a day. Defective items make up 2% of production. How many non-defective items are produced per day?

Show Answer

Total per day: 450×8=3600450 \times 8 = 3600. Defective: 3600×0.02=723600 \times 0.02 = 72. Non-defective: 3600−72=35283600 - 72 = \mathbf{3528}.

Problem 3: Tom earns $15/hour and works 6 hours on Saturday and 4.5 hours on Sunday. He spends 13\dfrac{1}{3} of his earnings on food. How much money does he have left?

Show Answer

Total hours: 6+4.5=10.56 + 4.5 = 10.5. Earnings: 10.5×15=157.5010.5 \times 15 = 157.50. Food: 157.50×13=52.50157.50 \times \frac{1}{3} = 52.50. Left: 157.50−52.50=105157.50 - 52.50 = 105. $105

Problem 4: A swimming pool is 50 m long, 25 m wide, and 2 m deep. Water fills 34\frac{3}{4} of the pool. How many litres of water are in the pool? (1 m³ = 1000 litres)

Show Answer

Full volume: 50×25×2=250050 \times 25 \times 2 = 2500 m³. Filled volume: 2500×34=18752500 \times \frac{3}{4} = 1875 m³. In litres: 1875×1000=1,875,0001875 \times 1000 = \mathbf{1{,}875{,}000} litres.

Summary​

  • Multi-step problems contain hidden sub-questions — identify them before calculating.
  • Use the 4-step strategy: Read → Plan → Solve → Check.
  • Key words signal the operation: total = add, difference = subtract, each = multiply, split = divide.
  • Always track units and apply operations in the correct order.
  • Re-read the question at the end to confirm your final answer addresses what was asked.

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