If you’re multiplying the sum of two numbers by a third number, you can multiply each number in your sum
individually. This comes in handy when you have to multiply the sum of two variables.
If a problem gives you information in “factored form”—a(b + c)—then you should distribute the first
variable before you do anything else. If you are given information that has already been distributed—(ab
- ac)—then you should factor out the common term, putting the information back in factored form. Very
often on the SAT, simply doing this will enable you to spot the answer.
Here are some examples:
Distributive: 6(53) + 6(47) = 6(53 + 47) = 6(100) = 600Multiplication first: 6(53) + 6(47) = 318 + 282 = 600You get the same answer each way, so why get involved with ugly arithmetic? If you use the distributive
law for this problem, you don’t even need to use your calculator.
The following drill illustrates the distributive law.
DRILL 2
Rewrite each problem by either distributing or factoring (Hint: For questions 1, 2, 4, and 5, try factoring)
and then solve. Questions 3, 4, and 5 have no numbers in them; therefore, they can’t be solved with a
calculator. Answers can be found on this page.
1. (6 × 57) + (6 × 13) =2. 51(48) + 51(50) + 51(52) =3. a(b + c – d) =4. xy – xz =5. abc + xyc =FRACTIONS
A Fraction Is Just Another Way of Expressing Division
The expression is exactly the same thing as x ÷ y. The expression means nothing more than 1 ÷ 2. In
the fraction , x is known as the numerator (hereafter referred to as “the top”) and y is known as the
denominator (hereafter referred to as “the bottom”).