Question

oscar has a map of the campground where he is staying. the scale shows that 4 inches on the map represents an actual distance of 2 miles. oscar’s tent is at campsite 4a. what number can you multiply each length on the map by to find the actual distance?

Explanation:

Step1: Understand the scale

The scale is 4 inches on the map represents 2 miles. We need to find the number (scale factor) to multiply map length by to get actual distance. So we calculate the ratio of actual distance to map distance.
Actual distance = 2 miles, Map distance = 4 inches. The ratio is $\frac{2}{4}=\frac{1}{2}$? Wait, no, wait. Wait, let's re - check. Wait, the scale is 4 in : 2 mi. So to find how many miles per inch, we do 2 miles / 4 inches = 0.5 miles per inch. But we can also think of it as for each inch on the map, what's the actual distance. But the question is "what number can you multiply each length on the map by to find the actual distance". So if map length is $x$ inches, actual distance $y$ (in miles) is $y = k\times x$, where $k$ is the scale factor. From 4 in (map) = 2 mi (actual), so $k=\frac{2}{4}=\frac{1}{2}$? Wait, no, wait 2 miles for 4 inches. So per inch, it's 2/4 = 0.5 miles per inch. But let's do it properly. Let's solve for $k$ in the equation: actual distance = $k$ × map distance. We know that when map distance is 4 inches, actual distance is 2 miles. So 2 = $k$×4. Solving for $k$, we divide both sides by 4: $k=\frac{2}{4}=\frac{1}{2}$? Wait, no, that would mean 4 inches × 1/2 = 2 miles, which is correct. Wait, but let's check with units. If map length is in inches, and we want actual distance in miles. So 4 inches (map) = 2 miles (actual). So the conversion factor is (2 miles)/(4 inches)= 0.5 miles per inch, or 1/2 miles per inch. So the number we multiply the map length (in inches) by to get actual distance (in miles) is 1/2? Wait, no, wait 4 inches map = 2 miles actual. So if we have a map length of $L$ inches, actual distance $D$ miles is $D=\frac{2}{4}\times L=\frac{1}{2}L$? Wait, but 4 inches times 1/2 is 2 inches, no, that's not right. Wait, I messed up. Wait, 4 inches on the map corresponds to 2 miles in real life. So to get from map inches to real miles, we use the ratio of real miles to map inches. So real miles = (2 miles / 4 inches) × map inches. So (2/4) simplifies to 1/2? Wait, no, 2 divided by 4 is 0.5. So 0.5 miles per inch. So if the map length is, say, 1 inch, actual distance is 0.5 miles. If map length is 4 inches, 4×0.5 = 2 miles, which matches the scale. So the number to multiply each length on the map by is 0.5, which is 1/2. Wait, but let's check the calculation again. Let's write the scale as a fraction: $\frac{\text{Actual Distance}}{\text{Map Distance}}=\frac{2\ \text{miles}}{4\ \text{inches}}=\frac{1}{2}\ \text{miles per inch}$. So the number $k$ is $\frac{1}{2}$. Wait, but let's confirm with the given scale. 4 inches (map) = 2 miles (actual). So if we have a map length of $x$ inches, actual distance $y$ miles is $y = \frac{2}{4}x=\frac{1}{2}x$. So the multiplier is $\frac{1}{2}$.

Step2: Verify

Take the map length of 4 inches. Multiply by 1/2: 4×(1/2)=2 miles, which matches the given scale (4 inches on map = 2 miles actual). So the number is 1/2. Wait, but let's check the units. The map length is in inches, and we want actual distance in miles. So the conversion factor is (2 miles)/(4 inches) = 0.5 miles per inch. So when we multiply a map length (in inches) by 0.5 (or 1/2), we get the actual distance in miles.

Answer:

$\frac{1}{2}$ (or 0.5)