To convert between units, you need to know the relationship between units. For example, one mile equals 5280 feet. This relationship can now be used as a conversion factor, set up as required by the question. For each conversion, choose the correct arrangement of the conversion factor and complete the calculation. 1. Convert 7860 feet to miles 7860 feet × ( A ) ( B ) A: Choose… B: Choose… 7860 feet= miles 2. Convert 0.565 miles to feet 0.565 miles × ( C ) ( D ) C: Choose… D: Choose… 0.565 miles= feet
The Correct Answer and Explanation is:
Convert 7860 feet to miles
Conversion Factor: 1 mile = 5280 feet
We want feet to cancel out and be left with miles.
So, set it up as: 7860 feet×(1 mile5280 feet)=78605280 miles7860\ \text{feet} \times \left( \frac{1\ \text{mile}}{5280\ \text{feet}} \right) = \frac{7860}{5280}\ \text{miles}7860 feet×(5280 feet1 mile)=52807860 miles
Calculation: 78605280≈1.4886 miles\frac{7860}{5280} \approx 1.4886\ \text{miles}52807860≈1.4886 miles
So:
- A = 1 mile
- B = 5280 feet
- Answer: 7860 feet = 1.49 miles (rounded to 2 decimal places)
2. Convert 0.565 miles to feet
Conversion Factor: 1 mile = 5280 feet
We want miles to cancel out and be left with feet.
So, set it up as: 0.565 miles×(5280 feet1 mile)=0.565×5280 feet0.565\ \text{miles} \times \left( \frac{5280\ \text{feet}}{1\ \text{mile}} \right) = 0.565 \times 5280\ \text{feet}0.565 miles×(1 mile5280 feet)=0.565×5280 feet
Calculation: 0.565×5280=2983.2 feet0.565 \times 5280 = 2983.2\ \text{feet}0.565×5280=2983.2 feet
So:
- C = 5280 feet
- D = 1 mile
- Answer: 0.565 miles = 2983.2 feet
Explanation:
Unit conversion is a common mathematical process that involves changing a quantity from one unit to another while maintaining its value. To do this properly, you need a conversion factor, which is a known equivalency between two units. For example, since 1 mile is exactly 5280 feet, you can use this as your base to convert between feet and miles.
In the first question, we are converting feet to miles. Because we want the final unit in miles, we arrange the conversion factor so that “feet” cancels out. This means placing 5280 feet in the denominator and 1 mile in the numerator, resulting in the setup:
7860 feet × (1 mile / 5280 feet).
Doing the division gives approximately 1.49 miles.
In the second question, we are converting from miles to feet. Here, we want miles to cancel out, so we arrange the conversion factor as 5280 feet over 1 mile. Multiplying gives
0.565 miles × (5280 feet / 1 mile) = 2983.2 feet.
The key idea is that when you multiply by a fraction that equals one (like 5280 feet / 5280 feet), you don’t change the value, only the unit. By ensuring the unwanted unit cancels, you are left with the correct unit in your answer. Always check the setup: the unit you want to cancel should be opposite (top vs. bottom) to where it starts.
