Maps with decimal distances

key notes :

Maps and Distances

• A map is a drawing that shows places and their positions.
• On a map, distances are shown using a scale (e.g., 1 cm on map = 2 km in real life).

Decimal Distances

• Distances in real life are not always whole numbers.
• We often use decimals to show smaller parts of a unit (like 2.5 km, 3.75 km, 12.4 km).

Using Scale with Decimals

Multiply the map measurement (in cm) by the scale to find the actual distance.

• Example: If scale = 1 cm = 1.5 km, and map distance = 4.2 cm →
• Actual distance = 4.2 × 1.5 = 6.3 km.

Adding and Subtracting Decimal Distances

When finding total distance (like two routes), add decimals.

• Example: 2.4 km + 3.65 km = 6.05 km.

Comparing Decimal Distances

Use place value to compare.

• Example: 7.25 km > 7.05 km because 25 hundredths > 5 hundredths.

Word Problems with Decimal Distances

Real-life problems often involve decimals in travel distances.

• Example: A person walks 3.5 km to school and 2.75 km to the market. Total distance walked = 3.5 + 2.75 = 6.25 km.

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📏 Examples

1. On a map, the distance between Town A and Town B is 6.4 cm.
   Scale: 1 cm = 2.5 km.
   → Actual distance = 6.4 × 2.5 = 16 km.
2. A road is 5.75 km long, and another road is 3.2 km long.
   Total = 5.75 + 3.2 = 8.95 km.
3. A student cycles 4.8 km, then walks 2.65 km.
   Total distance = 4.8 + 2.65 = 7.45 km.

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📝 Practice Questions

1. A map shows 7.2 cm between two villages. Scale = 1 cm = 1.8 km. What is the real distance?
2. A bus travels 12.5 km in the morning and 8.75 km in the evening. What is the total distance?
3. Which is farther: 9.05 km or 9.5 km?
4. The real distance is 24.6 km. On a map, the scale is 1 cm = 3 km. What is the map distance?
5. A person runs 2.45 km, then walks 1.85 km. What is the total distance?

Learn with an example