McGraw-Hill Education SAT 2018 Edition by Christopher Black & Mark Anestis

Author:Christopher Black & Mark Anestis
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2017-03-06T16:00:00+00:00

Which of the following is equivalent to 3(34 × 53)? [No calculator]

A) 3(34) × 3(53)

B) 94 + 153

C) 94 × 153

D) 35 × 53

Before making your choice, check the laws of arithmetic; don’t make up your own laws. Which laws of arithmetic can we use? Since the expression is a product, we can use the commutative law of multiplication and jumble up the terms, or the associative law of multiplication and regroup the terms any way we want (or not at all). Using the associative law gives us

3(34 × 53) = (3 × 34) × 53 = 35 × 53 Therefore, the correct answer is (D).

Don’t “over-distribute.”

Were you tempted to choose (A), (B), or (C) in the question above? If so, you are not alone. You are simply the victim of one of the most common mistakes in algebra: over-distribution. It comes from a misinterpretation of the Law of Distribution. The correct law is

When multiplying by a grouped sum, you don’t have to do the grouped sum first; you can multiply first, as long as you distribute the multiplication over the entire sum.

It is not

If something is outside parentheses, just bring it inside and distribute.

Look at these examples of “over-distribution” and verify that they are incorrect:

3(2 × 5) is not equal to (3 × 2) + (3 × 5) or (3 × 2) × (3 × 5)

(2 + 3)2 is not equal to 22 + 32

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