1.9 Properties of real numbers  (Page 4/10)

We conclude that there is no answer to $4÷0$ and so we say that division by 0 is undefined.

We summarize the properties of zero below.

We will now practice using the properties of identities, inverses, and zero to simplify expressions.

Now we will see how recognizing reciprocals is helpful. Before multiplying left to right, look for reciprocals—their product is 1.

Simplify expressions using the distributive property

Suppose that three friends are going to the movies. They each need $9.25—that’s 9 dollars and 1 quarter—to pay for their tickets. How much money do they need all together?

You can think about the dollars separately from the quarters. They need 3 times $9 so $27, and 3 times 1 quarter, so 75 cents. In total, they need $27.75. If you think about doing the math in this way, you are using the distributive property .

Back to our friends at the movies, we could find the total amount of money they need like this:

In algebra, we use the distributive property to remove parentheses as we simplify expressions.

For example, if we are asked to simplify the expression $3\left(x+4\right),$ the order of operations says to work in the parentheses first. But we cannot add x and 4, since they are not like terms. So we use the distributive property, as shown in [link] .