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All courses Math I · N-Q.1 47 of 59
Use units to guide multi-step problem solving and choose/interpret units, scales, and graph origins.

Convert units using a conversion factor

Problem
Convert 2 miles to feet for a race distance.
Your answer
Show answer choicesAnswer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
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Hint

Use the fact that 1 mile equals 5,280 feet.

To convert to a smaller unit, multiply by the number of smaller units in one larger unit.

Solution walkthrough

01

Write the conversion relationship

\[1~\text{mile}~=~5,280~\text{feet}\]

The prompt asks for the same race distance in feet. The given distance is 2 miles, and the needed conversion is 1 mile = 5,280 feet. This equality lets us replace each mile with 5,280 feet without changing the distance.

02

Arrange the factor to cancel miles

\[2~\text{miles}~×~(5,280~\text{feet}~/~1~\text{mile})\]

Use a conversion factor equal to 1: 5,280 feet divided by 1 mile. Multiplying the given 2 miles by this factor puts miles in both the numerator and denominator, so miles cancel and feet remain.

03

Calculate and check the conversion

\[2~×~5,280~=~10,560;~10,560~/~2~=~5,280\]

After the mile units cancel, multiply 2 by 5,280 to get 10,560 feet. Dividing 10,560 by the original 2 miles returns 5,280 feet per mile, so the result preserves the stated conversion rate.

04

State the race distance in feet

\[10,560~\text{feet}\]

The converted race distance is 10,560 feet, which exactly matches choice A.

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Another way

  1. View 2 miles as two equal 1-mile lengths: 5,280 feet + 5,280 feet = 10,560 feet.

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Common mistake

Do not stop at 5,280 feet. That is the length of one mile; the race is 2 miles, so the conversion amount must be multiplied by 2.