Application of map scale

### 1.1. Application of map scale

**Problem 1:** The map of Kindergarten in Thang Loi commune is drawn at a scale of 1:300.

On the map, the school gate is 2cm wide (Distance from A to B). What is the actual width of the school gate?

*Solution*

The actual width of the field gate is:

2 × 300 = 600 (cm)

600cm = 6m

Answer: 6m.

**Problem 2:** On a map with a scale of 1: 1 000 000, the distance between Hanoi and Hai Phong is measured at 102mm. Find the real length of the distance Hanoi – Hai Phong.

*Solution*

The distance from Hanoi to Hai Phong is:

102 × 1 000 000 = 102 000 000 (mm)

102 000 000mm = 102km

Answer: 102km.

### 1.2. Application of map scale (continued)

**Problem 1:** The distance between two points A and B on the school field is 20m. On a 1:500 scale map, how many centimeters is the distance between those two points?

*Solution*

20m = 2000cm

The distance between two points A and B on the map is:

2000 : 500 = 4 (cm)

Answer: 4cm.

**Problem 2:** The distance from Hanoi center to Son Tay is 41km. On a 1: 1 000 000 scale map, how many millimeters is that distance?

*Solution*

41km = 41 000 000mm

The distance from the center of Hanoi to Son Tay on the long map is:

41 000 000 : 1 000 000 = 41 (mm)

Answer: 41mm.

### 1.3. Textbook exercise solution page 157

**Lesson 1: **Write the correct number in the blank

Map scale |
1: 500 000 |
1: 15 000 |
1: 2000 |

Miniature length |
2cm |
3dm |
50mm |

True length |
… cm |
… dm |
… mm |

**Solution guide:**

With a map with a scale of 1: 500 000, to find the true length, we multiply the reduced length by 500 000.

The other sentences do the same.

Map scale |
1: 50000 |
1: 15 000 |
1: 2000 |

Miniature length |
2cm |
3dm |
50mm |

True length |
1 000 000cm |
45 000dm |
100 000mm |

**Lesson 2: **On the map of 1:200 scale, the length of my classroom is 4cm. What is the actual length of that classroom?

__Solution guide:__

- With a map with a scale of 1: 200, to find the true length, we multiply the reduced length by 2000.

*Solution*

The actual length of the classroom is:

4 x 200 = 800 (cm)

800cm = 8 m

Answer: 8m.

**Lesson 3: **On a map of 1: 2 500 000 scale, the distance between Ho Chi Minh City and Quy Nhon is 27cm. Find the real length of the distance between Ho Chi Minh City – Quy Nhon.

__Solution guide:__

- With a map with a scale of 1: 2 500 000, if you want to find the real length, we multiply the reduced length by 2 500 000. Then you can change to another unit to make the result more compact.

*Solution*

The distance between Ho Chi Minh City and Quy Nhon is:

27 x 250000 = 67500000 (cm)

67500000 cm = 675km.

Answer: 675km.

### 1.4. Textbook Exercises Page 158

**Lesson 1: **Write the correct number in the dot

Map scale |
1: 100000 |
1: 5000 |
1: 20000 |

Miniature length |
5 kilometres |
25m |
2km |

Length on the map |
… cm |
… mm |
… dm |

__Solution guide:__

- Convert the actual length measurement to the unit that measures the same as the miniature length unit.
- To find the length on the map, we take the actual length (with the unit of the reduced length) divided by the divisor in the map scale (for example, the map scale 1: 200, we will divide by 200. ).

5km = 50000cm

The length on the map is :

500000 : 10000 = 50 (cm)

25m = 25000mm

The length on the map is :

25000 : 5000 = 5 (mm)

2km = 20000m

The length on the map is:

20000 : 20000 = 1 (dm)

We have the following table:

Map scale |
1: 100000 |
1: 5000 |
1: 20000 |

True length |
5 kilometres |
25m |
2km |

Length on the map |
50cm |
5mm |
1dm |

**Lesson 2: **The distance from village A to village B is 12km long. On a 1:100 000 scale map, how many centimeters is that distance?

__Solution guide:__

- Convert the distance measurement to a unit with a measurement of centimeters.
- With a scale map of 1: 100 000, to find the length on the map of that distance, we take the actual length of that distance (with the unit of measurement being centimeters) divided by 100 000.

*Solution*

Change: 12km = 1200000cm

The distance from village A to village B on the map in centimeters is:

1200000 : 100000 = 12 (cm)

Answer: 12cm.

**Lesson 3: **A rectangular piece of land has a length of 15m and a width of 10m, drawn on a 1:500 scale map. On that map, how many centimeters is the length of each side of the rectangle?

__Solution guide:__

- Convert length and width measurements to centimeters.
- With a 1:500 scale map, to find the lengths on the map of the edges, we take the actual lengths of those edges (with the measurement unit being centimeters) divided by 500.

*Solution*

We have: 15m = 1500cm; 10m = 1000cm

The length of the rectangle on the map is :

1500 : 500 = 3 (cm)

The width of the rectangle on the map is:

1000 : 500 = 2 (cm)

Answer: Length: 3cm;

Width: 2cm.

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