# Units of Conversion: Linear Measure

Basic to the understanding of unit conversion is the understanding equivalence, the understanding of the multiplicative identity of 1, and how the two are related. For a review of these concepts, click on Review.

If you have forgotten how to manipulate fractions, visit Fractions for Adults on SOSMath for an in-depth review.

Review the following table (Webster's New World Dictionary, Second Edition, Simon and Schuster, 1982) of Standard Units of Conversion to see if you can create fractions that have a value of 1. You can click to examples following each table.

LinearMeasure

Example 1. Convert 4.6 miles to feet.

Solution.

• Write 4.6 miles as a fraction by dividing it by 1: .

• Multiply the fraction by 1:

• Note: We know that the fraction is equivalent to 1 because the numerator and the denominator measure the same length.

• Convert the number 1 in the expression to the equivalent fraction so that the expression can be written as

• Rewrite 4.6 miles as 4.6 x 1 mile and 5280 feet as 5280 x 1 foot, and rewrite the two fractions as

• Multiply the two fractions:

• Rearrange the numerator:

• Write the above fraction as two fractions:

• Replace the fraction by 1:

• Simplify:

If you would like to review another example, click on Example.

If you would like to practice some problems click on Problems.