Page 164 - ABCTE Study Guide_Neat

D 9 + 2 + 5 = 9 + 5 + 2 = 16

Answer

The correct answer is D. Although there are three numbers, it is still the order of the numbers that has
changed. This is the only answer choice in which the order of the numbers is different.

The last property that we’ll cover is the distributive property. The distributive property combines together
addition (or subtraction) and multiplication. The idea behind the distributive property is that it doesn’t
matter if you find the product of the sum/difference or the sum/difference of the product.

Algebraically, the distributive property is represented this way:

The distributive property comes in handy both in algebraic problems and in solving arithmetic problems
mentally. Let’s try a problem:

Can you multiply 9 x 47 in your head? Try it with the distributive property instead of replicating the paper-
and-pencil mentally.

Did you get 423? It should have worked this way:

First thought: 9 x 40 = 360

Second thought: 9 x 7 = 63

Third thought: 360 + 63 = 423

Not too hard, we hope. Try one more.

What is 15 x 34?

Did you get 510? Think 15(30 + 4) = 15 x 30 + 15 x 4 = 450 + 60 = 510

In algebra, the distributive property is often used to expand or simplify expressions so that an equation
can be solved. (Reversing the distributive property is called factoring, a topic that will be covered later in
this module.)

Let’s see how this works in practice. We’ll use the distributive property to simplify the expressions below.

6(x + 2y)

Distributing the 6, we arrive at 6x + 12y.

Here is one for you to try on your own.