Length — Grade 5 Mathematics
In Grade 5, we use all metric units with confidence, recognise approximate imperial equivalents, and solve complex multi-step length problems including those involving ratio and percentage.
Metric Length Conversions (Review)
| Conversion | Rule | Example |
|---|---|---|
| mm ↔ cm | ÷10 / ×10 | 85 mm = 8.5 cm |
| cm ↔ m | ÷100 / ×100 | 347 cm = 3.47 m |
| m ↔ km | ÷1000 / ×1000 | 6 820 m = 6.82 km |
Approximate Imperial Equivalents
Key approximate conversions (learn these):
• 1 inch ≈ 2.5 cm • 1 foot ≈ 30 cm • 1 yard ≈ 0.9 m
• 1 mile ≈ 1.6 km (or: 5 miles ≈ 8 km)
• 1 inch ≈ 2.5 cm • 1 foot ≈ 30 cm • 1 yard ≈ 0.9 m
• 1 mile ≈ 1.6 km (or: 5 miles ≈ 8 km)
💡 Miles to km: ×1.6; km to miles: ÷1.6 (or ×0.625). Using 8 km = 5 miles: 40 km ≈ 25 miles.
Worked Examples
Example 1 — Multi-Step Conversion
A track is 1.25 km long. An athlete runs 7 laps. How far in metres?
- 1.25 km × 7 = 8.75 km
- 8.75 km × 1 000 = 8 750 m
Example 2 — Miles to Kilometres
Convert 35 miles to km using the approximation 5 miles ≈ 8 km.
- 35 miles ÷ 5 = 7 groups
- 7 × 8 km = 56 km
Example 3 — Ratio Problem 📐
Two pieces of rope are in ratio 3 : 7. The total length is 4.5 m. Find each piece in cm.
- 10 parts total; 1 part = 4.5 ÷ 10 = 0.45 m
- Shorter: 3 × 0.45 = 1.35 m = 135 cm
- Longer: 7 × 0.45 = 3.15 m = 315 cm
Practice Questions
1. Convert 5.6 km to metres.
✅ 5.6 × 1 000 = 5 600 m
2. Convert 80 miles to km (use 5 miles = 8 km).
✅ 80 ÷ 5 = 16; 16 × 8 = 128 km
3. Add 3.48 km + 750 m. Give the answer in km.
✅ 750 m = 0.75 km; 3.48 + 0.75 = 4.23 km
4. A ladder is 3.2 m long. Each rung is 18 cm apart. How many rungs? (Ignore the top/bottom ends.)
✅ 3.2 m = 320 cm; 320 ÷ 18 ≈ 17.8 → 17 rungs (between 18 gaps; 17 rungs means 18 gaps)
5. A piece of string 7.5 m long is cut into pieces of 0.375 m each. How many pieces?
✅ 7.5 ÷ 0.375 = 7500 ÷ 375 = 20 pieces
Key Points to Remember
- Metric chain: mm × 10 → cm × 100 → m × 1 000 → km.
- 5 miles ≈ 8 km: a useful ratio to remember for conversions.
- 1 inch ≈ 2.5 cm; 1 foot ≈ 30 cm; 1 mile ≈ 1.6 km.
- Always convert to the same unit before adding or subtracting.
- Express answers in the unit requested in the question.