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Jan reads 50 pages every hour. How long will it take her to read a book with 673 pages?
When you're you aren't solving basic arithmetic or linear equations, you're more often than
not solving a proportion. From altering recipes to solving percents to finding unit rates
for cost comparison, proportions are one of the more ubiquitous problem types. Learning
how to solve them correctly will make your real-world adventures less painful.
A proportion is essentially a pair of equivalent fractions.
Proportions are useful for checking if two fractions are equivalent, or for creating
equivalent fractions.
They’re also useful for creating scale factors, unit rates, and percents.
If you want to use a proportion to see if two fractions are equivalent, set them equal
to each other.
Then cross multiply.
If you end up with the same product on both sides, the fractions are proportional and
equivalent. If you don’t, then they aren’t.
If you want to use a proportion to create equivalent fractions, which is what you’re
really doing when you solve proportions, start by setting up the problem.
Like things have to be in the same place in the proportion. For example, say you’re
trying to solve this problem.
We’re given the rate 12 miles in 2 hours, so that’s our first fraction. We want to
know how many miles she’ll walk in 4 hours. Because 2 hours is in the denominator of the
first fraction, we’ll put 4 hours in the denominator of the second fraction. We’re
keeping like items in the same location.
Do we have to set it up this way? No, we don’t. We could take the two hours values and set
them up as the first fraction. Then we set 12 in the numerator of the second fraction
because the 2 hours is in the numerator of the second fractions. Again, we’re keeping
like things together.
If you’re ever unsure if you have your proportion set up correctly, just start labeling. It
becomes clear pretty quickly when you’ve mismatched numbers.
Once you have everything in its proper place, cross multiply and solve for the variable.
How long will Jan spend reading this book?
Set up the correct proportion and then solve it.
It will take her right around 13 hours and 28 minutes.
When solving a proportion, cross-multiply and solve for the variable.