To determine how many miles [tex]\( 3 \frac{3}{4} \)[/tex] inches represent on a map where 1 inch equals 92 miles, let's break down the problem into smaller steps:
1. Express the mixed number as an improper fraction or a decimal:
[tex]\( 3 \frac{3}{4} \)[/tex] inches can be rewritten as a decimal or an improper fraction.
[tex]\[
3 \frac{3}{4} = 3 + \frac{3}{4} = 3 + 0.75 = 3.75 \text{ inches}
\][/tex]
2. Assume the scale is such that 1 inch is equivalent to 92 miles:
We need to find out how many miles [tex]\( 3.75 \)[/tex] inches would represent.
3. Set up the multiplication:
Since 1 inch is 92 miles, we multiply the number of inches by the number of miles per inch.
[tex]\[
3.75 \text{ inches} \times 92 \text{ miles per inch}
\][/tex]
4. Perform the multiplication:
[tex]\[
3.75 \times 92 = 345 \text{ miles}
\][/tex]
Thus, [tex]\( 3 \frac{3}{4} \)[/tex] inches represent 345 miles on the map.
Answer: [tex]\( 3 \frac{3}{4} \)[/tex] inches represent 345 miles.
