
Ratios
Math teachers love to use pizza slices to teach fractions
and ratios. Who are we to argue with tradition? Consider a humble
eightslice pizza. You eat three pieces, and your imaginary buddy,
Kronhorst, eats the other five. (Imaginary friends don’t have to
worry about gaining weight.) The fraction of the pizza you ate can
be determined by the part you ate over the whole number
of slices. That’s what fractions are, a part to a whole.
Ratios compare parts to parts.
The ratio of pieces you ate to the pieces Kronhorst ate is 3:5,
because it compares the part you ate to the part Kronhorst ate.
The ratio can be written as 3:5 or or ratio
of 3 to 5. Even though looks
like a fraction, it’s not. The bottom number is not a
denominator.
If the ratio of A to B is
3:4, this does not necessarily mean that there are 3 pieces of A and
4 pieces of B. There could be 6 pieces of A and
8 pieces of B for a ratio of 6:8, which then reduces
down to 3:4. Ratios don’t always tell you the actual amount, but
they do allow you to compare one object to another:

First find the ratio of those who buy books online to
those who buy books at bookstores. This ratio can be written as
50:10.
You can simplify ratios the same way fractions are simplified:
50:10 = 5:1, choice D.
For every 5 people who buy books online, 1 person actually
goes to the bookstore and buys a book. Whether that person actually
reads it is another issue.
Proportions
Some items not only require knowledge of ratios but also
test your ability to figure out the actual values from the ratios.
For instance, look at this item:

You immediately know that for every 5 gray ties
there are 7 black ones and 3 brown ones. You also know that for
every 15 ties (7 + 5 + 3), 5 ties are gray and that the total number
of ties is 45. Keep in mind that the ratios do not change,
no matter the total number of objects. This helps you set up a proportion—an equation
based on the notion that two ratios are equal.
5:15 is the same as x:45. To solve for x:
Now cross multiply to get:
455 = 15x
225 = 15x
x = 15
The total number of gray ties is 15, choice D.
