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The way I like to think about it. Multiplying by dimensionless one (1) does not change the mass (just how it is expressed). Think about equivalent fractions.

1/7 is the same as 3/21. If you multiply 1/7 by (3/3), then you get 3/21.

3/3 is equivalent to 1, so the value has not changed just how you express it.

Take 6 ounces mass, and you want to convert to pounds mass.

1 pound = 16 ounces, so divide both sides of this equality by (16 ounces):

(1 pound) / (16 ounces) = 1 (dimensionless)

So multiply (6 ounces) by [(1 pound) / (16 ounces)], or divide by [16 ounces / pound], does not change the mass you have, just how you express it.

(6 ounces) / (16 ounces / pound) = 3/8 pound = 0.375 pound.

Sometimes it's easier to do if you draw a line (representing the 'bar' of a fraction, and place the conversion factors so that units cancel:

1 pound | 6 ounces

------------------------- = 0.375 pounds

16 ounces| 1

The 'ounces' cancel and you are left with pounds. The vertical lines are just an easy way to separate your terms. After the units are canceled out and simplified, multiply all the values in numerator, then divide by all values in denominator. You can have a long line with several terms to work with and it really helps keep track of things.

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14y ago

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