Answer:
Step-by-step explanation:
a) You're interested in the percentage represented by the ratio ...
$3750/$5000
To convert any ratio or fraction to a percentage, multiply it by 100%:
$3750/$5000 × 100% = 75%
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b) This and the next are essentially division problems. To find the number of times a larger quantity can be made into smaller quantities, divide the larger quantity by the smaller. You can see this if you write and solve an equation:
24 cups = n × (2/3 cup)
24/(2/3) = n . . . . . . . . . . . . . divide by the coefficient of n; units of cups cancel
24×(3/2) = n = 36
Jane will take 36 days to finish the cereal.
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c) Same approach as the previous problem:
21 in = n × (1 3/4 in)
21/(7/4) = n . . . . . . . . divide by the coefficient of n; units of inches cancel
21×(4/7) = n = 12
There are 12 boards in the stack.
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<em>Comment on units</em>
If you keep the units with the numbers, the units of the answer will come out right if you did the arithmetic properly. If the answer units don't make sense, you have probably formulated the problem incorrectly.
For the last two problems, we have cancelled the units, so have an answer that is a "pure number"--one with no units. Such an approach is suitable when the answer is a count of something. We could have used some additional units, such as ...
(24 cups/box)/(2/3 cup/day) = 36 day/box
(21 in/stack)/(7/4 in/board) = 12 board/stack
The "/" is read as "per": 36 days per box, or 12 boards per stack. If you use these "extended" units, there is almost no way to do the math wrong and have the units of the answer make sense. (Consideration of the units can help you figure out what math you need to do to end up with the proper units.)
Math with units is similar to math with any variable(s). They can be multiplied, divided, added, subtracted, raised to a power--just like variables are. As with variables, you can only add or subtract "like" units.
Using units is <em>helpful</em> with many math "word problems." It is <em>essential</em> for most physics and healthcare (dosage) problems.
