The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 2.19: Converting from One Unit

of Measurement to Another Using the Multiplication

Property of One

A common mistake students make when converting from one unit of measurement to another is

dividing when they should multiply or multiplying when they should divide. Understanding the

multiplication property of one can reduce the incidence of this mistake.

1. Review the multiplication property of one with your students: The product of one and any
   number is equal to the original number.


2. Explain that to use the multiplication property of one for conversions, students will work
   with fractions. The number 1 can be represented as a fraction in several ways. Offer these
   examples:

1 foot

12 inches

,

12 inches

1 foot

,

1000 meters

1 kilometer

. Note that the numerator and denominator of
each fraction represent the same value.
3. Review the example on the worksheet with your students. Point out that the ‘‘inches’’ in the
fractions cancel each other out, leaving ‘‘yard’’ as the unit of measure. Note that students
must understand equivalences to complete measurement conversions. If necessary, suggest
they use reference tables, which are usually included in math texts.
4. Explain that there may be other ways to complete conversions. For example, converting
3 inches to feet can easily be done by writing a fraction and simplifying. Because 12 inches=
1 foot,

3

12

=

1

4

. Therefore, 3 inches=

1

4

foot.

EXTRA HELP:

Double-check conversion facts and be sure answers are in terms of the correct unit.

ANSWER KEY:

(1)36 inches (2) 1

1

4

feet (3)

1

10

mile (4)48 ounces (5) 2

1

2

cups (6)3quarts

(7) 2

1

4

gallons (8)0.064 or

8

125

kilometer

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(Challenge)Mariano is correct. Explanations may vary. To convert 18 inches to feet, you must

divide 18 by 12 because 12 inches equal 1 foot. 18 inches equals 1

1

2

feet. To convert 2 yards to

feet, you must multiply 2×3. Because 3 feet equal 1 yard, 2 yards equal 6 feet.

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