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All courses Math Foundations · MF.GM.1 48 of 60
Convert measurements within a system and use unit reasoning to choose the correct scale.

Convert to a smaller unit

Problem
Convert \(3~\text{feet}\) to inches.
Your answer
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Hint

Write the unit fact you need first: 1 foot = 12 inches.

You are converting from a larger unit to a smaller unit, so the number gets larger. For feet to inches, multiply by 12.

Solution walkthrough

01

Use the feet-to-inches conversion

\[1~\text{foot}=12~\text{inches}\]

Each foot contains twelve inches.

02

Set up a unit-canceling product

\[3~\text{feet}~\times~(12~\text{inches}/1~\text{foot})\]

Put feet in the denominator of the conversion factor so the original unit cancels.

03

Calculate

\[3\times~12=36\]

Three groups of twelve inches total thirty-six inches.

04

Check reasonableness

\[\text{inches}~\text{are}~\text{smaller}~\text{than}~\text{feet}~⇒~\text{numerical}~\text{measure}~\text{should}~\text{increase};~36>3\]

The larger number is sensible when expressing the same length in a smaller unit.

05

Report the converted length

\[36~\text{inches}\]

Three feet and thirty-six inches describe the same length.

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Another way

  1. Add 12+12+12 inches for the three feet.

!

Common mistake

Do not divide by twelve; converting from larger feet to smaller inches increases the numerical measure.

Solution walkthrough video