Math Help for Section 3.4, Page 129
Setting
Up Ratios
If you use different units of measurement in the numerator and
denominator of a ratio, then you must include the units. If you use the
same units of measurement in the numerator and denominator, then it is
not necessary to write the units.
To make sure the numerator and denominator of a ratio have the same
unit of measurement, you will often have to convert one of them. To
convert a measurement, multiply it by the ratio of two equivalent
measurements. For instance, since 1 foot is equal to 12 inches, you can
multiply a measurement by
$\displaystyle{{12{\text{ inches}}} \over
{1{\text{ foot}}}}$ or $\displaystyle{{1{\text{ foot}}} \over
{12{\text{ inches}}}}$
to change the units without changing the value of the original
measurement. During or after the multiplication, divide out like units
using unit analysis. You can use this technique to convert 4 feet to 48
inches and to convert 8 inches to $8 \over {12}$ foot.
| $\displaystyle 4{\text{ feet}} = 4{\cancel{\text{feet}}} \bullet {{12{\text{ inches}}} \over {1{\cancel{ \text{foot}}}}} = 48{\text{ inches}}$ |
| $\displaystyle 8{\text{ inches}} = 8{\cancel{ \text{inches}}} \bullet {{1{\text{ foot}}} \over {12{\cancel{ \text{inches}}}}} = {8 \over {12}}{\text{ foot}}$ |
To see a list of conversions, refer to the inside of the back cover of the textbook.
Example
2: Tip
| b. | You can convert 3 meters to $3(100)$ centimeters as follows. |
| $\displaystyle 3{\text{ meters}} = 3{\cancel{ \text{meters}}} \bullet {{100{\text{ centimeters}}} \over {1{\cancel{ \text{meter}}}}} = 3\left( {100} \right){\text{ centimeters}}$ |
|
| c. | You can convert 200 cents to 2 dollars as follows. |
| $\displaystyle 200{\text{ cents}} = 200{\cancel{ \text{cents}}} \bullet {{1{\text{ dollar}}} \over {100{\cancel{ \text{cents}}}}} = 2{\text{ dollars}}$ |
|
| d. | You can convert $1{1 \over 2}$ years to 18 months as follows. |
| $\displaystyle 1{1 \over 2}{\text{ years}} = 1{1 \over 2}{\cancel{\text{years}}} \bullet {12{\text{ months}} \over {1{\cancel{\text{year}}}}} = 18{\text{ months}}$ |