Blog

SAT Math: Arithmetic

Distributive Law

84 + 85 = ?

A. 89
B. 820
C. 8(16)
D. 9(84)
E. 169

Knowsys Method

Read the question carefully.  It may sound funny to say this when there are no words, but do not skip this step!  Many students are used to adding exponents together.  This will get you the wrong answer in this problem!  You can only add exponents together when you are multiplying.  You cannot add exponents when you are adding.  

Identify the bottom line.  In this case you only need to solve the problem.

 Assess your options.  You could try to come up with an answer by  multiplying 8 by itself 4 times and adding it to 8 multiplied by itself 5 times, but that will take a long time.  Glance at the answers.  None of them are actually numbers.  You need to simplify the equation by manipulating it and finding out what each added part has in common with the other.  To do that, you must use the distributive law.  Normally you use the distributive law when you have variables: a(b + c) = ab + ac.  However, it applies to any problem with addition.

 Attack the problem.  Think about the problem in terms of what the exponents actually mean.  If you have four 8s multiplied together and five 8s multiplied together, what do they share in common?  The answer is four 8s.  You can pull out four 8s from both sides of the addition sign:

84 + 85 =
84(1 + 8)=
84(9)

Does that answer look like one of your answer choices?  Yes! 

Loop back.  You simplified this problem as much as possible.  Select your answer.

 

The correct answer is (D). 

This is a medium level question. 

 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email