To convert a distance of 12,000 feet to miles, which ratio could you multiply by?
A. [tex]$\frac{1 \text { mile }}{5280 \text { feet }}$[/tex]
B. [tex]$\frac{1 \text { foot }}{5280 \text { miles }}$[/tex]
C. [tex]$\frac{5280 \text { feet }}{1 \text { mile }}$[/tex]
D. [tex]$\frac{12 \text { inches }}{1 \text { foot }}$[/tex]
Answer (2)
To convert feet to miles, multiply by a ratio with miles in the numerator and feet in the denominator.
The correct ratio is 5280 feet 1 mile .
Multiplying 12,000 feet by this ratio converts it to miles.
The answer is A. 5280 feet 1 mile
Explanation
Understanding the Problem We are given a distance of 12,000 feet and asked to convert it to miles. We need to choose the correct ratio to multiply by to perform this conversion. The key is to use a ratio where the units of feet cancel out, leaving us with miles.
Setting up the Conversion To convert feet to miles, we need a conversion factor that has miles in the numerator and feet in the denominator. This way, when we multiply 12,000 feet by the conversion factor, the 'feet' units will cancel out, and we will be left with 'miles'.
Analyzing the Options Let's examine the given options:
A. 5280 feet 1 mile - This has miles in the numerator and feet in the denominator, which is what we want. B. 5280 miles 1 foot - This has feet in the numerator and miles in the denominator, which is the inverse of what we need. C. 1 mile 5280 feet - This has feet in the numerator and miles in the denominator, which is also the inverse of what we need. D. 1 foot 12 inches - This converts feet to inches, not feet to miles.
Applying the Correct Ratio Option A, 5280 feet 1 mile , is the correct ratio. When we multiply 12,000 feet by this ratio, we get:
12000 feet × 5280 feet 1 mile = 5280 12000 miles
Final Answer Therefore, the correct ratio to multiply by is 5280 feet 1 mile .
Examples
Imagine you're planning a road trip and the navigation system gives distances in feet, but you prefer to think in miles. Knowing the conversion factor between feet and miles allows you to quickly understand the distances involved. For example, if the system says the next town is 10,560 feet away, you can easily convert this to 2 miles by multiplying 10,560 feet by the ratio 5280 feet 1 mile . This makes it easier to estimate travel time and plan your journey effectively.
To convert 12,000 feet to miles, you should use the ratio 5280 feet 1 mile : option A. This ratio cancels out feet and leaves you with miles. Thus, 12,000 feet is approximately 2.27 miles.
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