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A
=
l●w
The formula in this case will only “eat” units that are associated with distance. You would not say a rectangle is three gallons long, but you might say it is three feet long.
Take a look at the speed formula as well.
speed
=
distance
time
This formula would need units that measure distance in the numerator, and units that measure time in the denominator.
The units for the result of the formulas will depend on what units you “feed” it. Formulas are what they eat!
•For the area formula, if the units of feet (ft) were used for the length and width, then the area would be measured in square feet. •Since x ● x = x2, then it follows that ft ● ft = ft2.
•The same goes for all units of measure, square meters (m2), square inches (in2), or square centimeters (cm2).
•For the speed formula, if the unit of meters was used for the distance and the unit of seconds was used for the time, then the speed would be measured in meters per second. •Division requires the use of the word “per” in the unit. Miles divided by hours equals miles per hour.
1 gallon is equal to 128 fluid ounces.
5 gallons●
128 fluid onces
1 gallon
=
640 fluid ounces
The paint-sprayer can handle 100 fluid ounces at a time, since Daniel has 640 fluid ounces (5 gallons) he would be able to fill it up 6 times.
640
100
=
6.4
1 fluid ounce is equal to 0.0078125 gallons.
100 fluid ounces
0.0078125 gallons
1 fluid ounce
=
0.78125 gallons
The paint-sprayer can handle 0.78125 gallons.
5
0.78125
=
6.4
The fraction of fluid ounces per gallon is referred to as a conversion ratio. This ratio can be derived from the conversion table linked above. On the table, it lists that 1 gallon = 128 fluid ounces. Daniel is converting from gallons to fluid ounces, so he correctly places the gallon information in the denominator of the ratio.
The ratio is set up this way so that the units will cancel out, leaving the units required.
Observe that the unit of gallon is in both the numerator and denominator. The unit of gallon can be canceled out.
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