Lesson 24: Decimal Word Problems

§Text Passage

1Summary 重點摘要

Decimal mixed operations: shopping change, sharing, unit conversion, concentration. Learn to turn word problems into number sentences.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: Shopping ChangeChange problems use subtraction: money paid - cost = change. Example: shopping costs $28.5, you pay $50, and 50.0 - 28.5 = 21.5, so the change is $21.5. Write 50 as 50.0 and line up the decimal points before subtracting to keep every digit in its place. If you pay $100 for goods of $28.5, work out 100.0 - 28.5 = 71.5 and the change is $71.5; larger amounts use the same method — the key is always padding zeros and lining up the points.
2. Block 2: Sharing MoneySharing money equally uses division: total ÷ number of people = share each. Example: 4 classmates buy a $128.8 gift together, and each pays 128.8 ÷ 4 = $32.2. Handle the whole part and the decimal part in turn, keeping the quotient's point aligned with the dividend's. Check by multiplying one share back: 32.2 × 4 = 128.8, matching the total, so the division is right; if it does not divide exactly, round to the decimal places the question asks for.
3. Block 3: Unit Conversion (Length)Length units connect closely with decimals: 1 m = 100 cm. Metres to centimetres multiplies by 100 — 2.5 m = 250 cm and 0.8 m = 80 cm; centimetres to metres divides by 100 — 150 cm = 1.5 m. Metre-centimetre conversion is the most common, so keep the direction straight. Rule of thumb: to a smaller unit, multiply by the rate; to a bigger unit, divide by it — for example 0.06 m = 6 cm, and 30 mm = 3 cm.
4. Block 4: Unit Conversion (Weight)Weight works the same way: 1 kg = 1000 g. Kilograms to grams multiplies by 1000 — 3.2 kg = 3200 g and 0.45 kg = 450 g; grams to kilograms divides by 1000 — 750 g = 0.75 kg. The point shifts three places: left for the bigger unit, right for the smaller. Combined forms are common too: 1 kg 250 g = 1.25 kg, and 2.08 kg = 2 kg 80 g.
5. Block 5: Mixed CalculationHarder word problems are written in steps. Example: 2 packs of biscuits at $8.5 each, pay $20 — how much change? Step one, the total: 2 × 8.5 = $17; step two, the change: 20 - 17 = $3. Writing each step separately, one job per line, keeps the working clear. If you pay $50 for those two packs, the change = 50 - 17 = $33; in multi-step questions, write out each step's working and result so the work can be checked along the way.
6. Block 6: Concentration (Intro)Example: 500 mL of water has 25 g of sugar dissolved in it — how much sugar in every 100 mL? Since 500 mL is 5 times 100 mL, split the sugar into 5 equal parts: 25 ÷ 5 = 5 g, so every 100 mL holds 5 g. Find the size factor first, then share the amount out in that ratio. To find the sugar in every 50 mL, halve again: 5 g ÷ 2 = 2.5 g, since 100 mL is twice 50 mL; convert to a per-100 mL amount first, then scale — the safest line of thought.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Word problems: read the question first
• Change: paid - total
• Sharing: total ÷ people
• 1 m = 100 cm; 1 kg = 1000 g
• Multiply/divide before add/subtract