Noah is looking at a map of his neighborhood that has a scale of 1 to 300.

On this map the distance from Noah's house to the school is 5 centimeters.
 
Noah doesn't like the size of this map and is going to make a new one with a scale of 1 to 150.

On the new map what is the distance from Noah's house to the school?

To solve this problem, we need to compare the two map scales and find out how the distance between Noah's house and the school will change on the new map.

The current map scale is 1:300, meaning that 1 cm on the map corresponds to 300 cm in reality. The distance from Noah's house to the school on the current map is 5 cm. This means the real-life distance is:

\[
\text{Real-life distance} = 5 \, \text{cm} \times 300 = 1500 \, \text{cm}
\]

Noah is creating a new map with a scale of 1:150. So, 1 cm on the new map will correspond to 150 cm in reality. To find the distance on the new map, we divide the real-life distance by the new map scale:

\[
\text{New map distance} = \frac{1500 \, \text{cm}}{150} = 10 \, \text{cm}
\]

Therefore, on the new map, the distance from Noah's house to the school will be **10 centimeters**.

Would you like a detailed breakdown of the steps or have any questions?

Here are 5 related questions to explore further:
1. How would the distance change if the new map scale was 1:200?
2. What is the actual distance in meters between Noah's house and the school?
3. How would the scale change if Noah wanted the distance to appear as 7.5 cm on the new map?
4. If the real-life distance was 3 km, what would be the map distance at a 1:300 scale?
5. How does changing the scale affect the area of objects shown on the map?

**Tip:** When working with scales, remember that they are ratios that relate map measurements to real-world distances. Smaller numbers in the scale mean larger representations on the map.

Noah is looking at a map of his neighborhood that has a scale of 1 to 300. On this map the distance from Noah's house to the school is 5 centimeters. Noah doesn't like the size of this map and is going to make a new one with a scale of 1 to 150. On the new map what is the distance from Noah's house to the school?

Learn how to calculate the distance on a new map when the scale changes from 1:300 to 1:150. This problem demonstrates the use of scale factors and proportions to solve real-world mapping problems. Suitable for students in Grades 5-7.

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