In word problems (which most SAT problems are), certain English words usually
refer to certain basic operations.
Of usually means multiply: ½ of y means ½ × y.
Exceeds by or is greater than usually means subtract (or add): x exceeds y by
7 means x – y = 7 (or y + 7 = x).
Total or altogether usually means addition: the total of x and y means x + y.
Each usually means multiply (or divide): 20 baskets, each with 12 eggs,
means you have 20 × 12 eggs, or 240.
MENTAL MATH TRICK 7: NO CALCULATOR FOR FRACTIONS
This is less a trick than a warning. Before we tell you all about fractions, it’s
important to know that calculators are not great at handling fractions. On a non-
graphing calculator, you have to first convert fractions to decimals, which is an
added step. On a graphing calculator, you have to bracket your fractions in
parentheses, which creates a ballroom-size room for error.
SOME ARITHMETIC REMINDERS
As we said, the SAT breaks down its math problems into four major categories,
Problem Solving and Data Analysis, Heart of Algebra, Passport to Advanced
Math, and Additional Topics. Before we get into those areas, we need to review
two basic arithmetic concepts that are heavily involved in all of those areas:
fractions and negative numbers.
Fractions and Their Meaning
Now, we know you’ve seen a lot of fractions in math class, and you know more
or less how to work with them. But the SAT requires that you know what a
fraction means. You need to understand that ⅗ not only means three-fifths, but
also 3 divided by 5. You need to understand that miles/hour means miles divided
by hours. If this feels a little iffy, then read this section carefully because this is
one of the most important ideas on the Math SAT.
The following problem will illustrate why three-fifths and 3 divided by 5 are
the same thing.
THE QUICHE PROBLEM
Rihanna, Madonna, Beyoncé, an accountant named Merle, and Sia are having
breakfast together. They order three quiches, which they plan to divide equally.