Question

1. a map of a park has a scale of 1 inch to 1,000 feet. another map of the same park has a scale of 1 inch to 500 feet. which map is larger? explain or show your reasoning.

Explanation:

Step1: Understand scale concept

The scale represents the ratio of map - distance to real - world distance. A smaller denominator in the ratio means a larger map.
For the first map, the scale is 1 inch : 1000 feet, or $\frac{1}{1000}$ inches per foot.
For the second map, the scale is 1 inch : 500 feet, or $\frac{1}{500}$ inches per foot.

Step2: Compare the ratios

We compare the fractions $\frac{1}{1000}$ and $\frac{1}{500}$.
Since $\frac{1}{500}>\frac{1}{1000}$ (when the numerators are the same, the fraction with the smaller denominator is larger).

Answer:

The map with a scale of 1 inch to 500 feet is larger.