When converting 7 feet to inches, what conversion fraction do you use?
The correct answer and explanation is:
The conversion fraction used when converting feet to inches is:
1 foot = 12 inches
So the conversion fraction is: 12 inches1 foot\frac{12 \text{ inches}}{1 \text{ foot}}
This fraction means that for every 1 foot, there are 12 inches.
Explanation
When converting between units, a conversion fraction or factor relates one unit to another. In this case, feet and inches are both units of length used in the customary system. Since 1 foot equals exactly 12 inches, this relationship serves as the conversion factor.
To convert 7 feet to inches, multiply the number of feet by the conversion fraction that cancels out feet and leaves inches. The fraction 12 inches1 foot\frac{12 \text{ inches}}{1 \text{ foot}} does this because “feet” in the denominator cancels with the “feet” unit in the original measurement, leaving inches as the result.
Mathematically: 7 feet×12 inches1 foot=7×12 inches=84 inches7 \text{ feet} \times \frac{12 \text{ inches}}{1 \text{ foot}} = 7 \times 12 \text{ inches} = 84 \text{ inches}
This process uses multiplication by a fraction equal to one in value but different in units. Multiplying by this fraction changes the units without changing the actual length.
It is important to use the correct conversion fraction to avoid errors. If the fraction were reversed, for example, 1 foot12 inches\frac{1 \text{ foot}}{12 \text{ inches}}, the calculation would convert inches to feet instead.
Conversion fractions are a fundamental tool in unit conversions in science, engineering, and everyday measurements. They allow smooth transitions between units by establishing fixed ratios between them. In this case, using the fraction 12 inches1 foot\frac{12 \text{ inches}}{1 \text{ foot}} correctly converts a length given in feet into inches.