To convert a distance of 1.7 miles to feet, which ratio could you multiply by?
A. [tex]$\frac{1 \text { foot }}{5280 \text { miles }}$[/tex]
B. [tex]$\frac{1 \text { mile }}{5280 \text { feet }}$[/tex]
C. [tex]$\frac{12 \text { inches }}{1 \text { foot }}$[/tex]
D. [tex]$\frac{5280 \text { feet }}{1 \text { mile }}$[/tex]
Answer (1)
Analyze the units: To convert miles to feet, the ratio must have feet in the numerator and miles in the denominator.
Evaluate the options: Only option D, 1 mile 5280 feet , has the correct unit placement and numerical values.
Apply the ratio: Multiplying miles by 1 mile 5280 feet correctly converts the distance to feet.
The correct ratio is: 1 mile 5280 feet
Explanation
Understanding the Problem We are given a distance of 1.7 miles and asked to convert it to feet. We need to identify the correct ratio to multiply by to perform this conversion.
The Conversion Strategy The key to converting units is to use a ratio where the units you want to convert from are in the denominator and the units you want to convert to are in the numerator. This way, the original units will cancel out, leaving you with the desired units.
Analyzing the Options Let's examine each option:
A. 5280 miles 1 foot : This ratio has feet in the numerator and miles in the denominator, which is the correct setup. However, the numbers are inverted. We know that 1 mile is equal to 5280 feet, not the other way around.
B. 5280 feet 1 mile : This ratio has miles in the numerator and feet in the denominator, which is the opposite of what we need. Multiplying by this ratio would convert feet to miles, not miles to feet.
C. 1 foot 12 inches : This ratio relates inches to feet. While it's a valid conversion factor, it's not relevant to converting miles to feet directly.
D. 1 mile 5280 feet : This ratio has feet in the numerator and miles in the denominator, and the numerical values are correct (5280 feet = 1 mile). This is the ratio we need.
Performing the Conversion To convert 1.7 miles to feet, we would multiply 1.7 miles by the ratio 1 mile 5280 feet :
1.7 miles × 1 mile 5280 feet = 8976 feet
The miles unit cancels out, leaving us with the answer in feet.
Final Answer Therefore, the correct ratio to multiply by is D. 1 mile 5280 feet .
Examples
Imagine you're planning a cross-country road trip and want to know how many feet you'll be driving. If the total distance is 2500 miles, you can use the conversion factor 1 mile 5280 feet to find the distance in feet: 2500 miles × 1 mile 5280 feet = 13 , 200 , 000 feet . This helps you appreciate the scale of the journey and could be useful for calculations like fuel consumption or estimating travel time.
