To determine how many miles [tex]$4 \frac{5}{4}$[/tex] inches represent on a map where 1 inch equals 80 miles, follow these steps:
1. Convert the mixed number to an improper fraction or a decimal:
First, we need to convert [tex]$4 \frac{5}{4}$[/tex] inches into a single numerical value.
- The mixed number [tex]$4 \frac{5}{4}$[/tex] can be converted to an improper fraction:
[tex]\[
4 \frac{5}{4} = 4 + \frac{5}{4}
\][/tex]
- Convert the 4 into a fraction with the same denominator for easy addition:
[tex]\[
4 = \frac{4 \times 4}{4} = \frac{16}{4}
\][/tex]
- Now add the two fractions:
[tex]\[
\frac{16}{4} + \frac{5}{4} = \frac{16 + 5}{4} = \frac{21}{4}
\][/tex]
Therefore, [tex]$4 \frac{5}{4}$[/tex] inches is equivalent to [tex]$\frac{21}{4}$[/tex] inches.
- Alternatively, as a decimal:
[tex]\[
4 + \frac{5}{4} = 4 + 1.25 = 5.25
\][/tex]
So, [tex]$4 \frac{5}{4}$[/tex] inches equals 5.25 inches.
2. Calculate the number of miles:
To find out how many miles [tex]$4 \frac{5}{4}$[/tex] inches represent, we use the scale given that 1 inch represents 80 miles.
Multiply the number of inches by the number of miles per inch:
[tex]\[
\text{Miles} = 5.25 \times 80
\][/tex]
3. Perform the multiplication:
[tex]\[
5.25 \times 80 = 420
\][/tex]
Therefore, [tex]$4 \frac{5}{4}$[/tex] inches on the map represent 420 miles.
So, the answer is that [tex]$4 \frac{5}{4}$[/tex] inches represent 420 miles.
