In the previous lesson we learned about variables, expressions, and equations. Let’s take a quick review.

Click the “Submit” button after selecting your answer.

Now, let's continue with today's lesson.

We are already familiar with the basic number operations: addition, subtraction, multiplication, and division. Let's take a look at each one.

The addition operation is indicated by the 'plus' sign.

The expression "five plus four" means 5 + 4.

If we carry out the addition operation in this expression, what is the resulting value? Click the “Submit” button after entering your answer.

In carrying out the addition, we say that the expression evaluates to nine.

The answer to an addition operation is known as the sum.

The subtraction operation is indicated by the 'minus' sign.

The expression "ten minus three" means 10 - 3.

To what does this expression evaluate? Click the “Submit” button after entering your answer.

The answer to a subtraction operation is known as the difference.

Addition and subtraction are inverse operations. We can arrive at the same result by thinking of the expression as adding - 3 to 10.

Whenever we add two real numbers, the result is always a real number. This is referred to as the closure property of addition.

The multiplication operation is indicated by the 'multiplication' symbol.

It also may be indicated by using a 'dot' symbol or parentheses.

The expression "two times thirteen" means <EQUATION>.

To what does this expression evaluate? Click the “Submit” button after entering your answer.

The answer to a multiplication operation is known as the product.

The division operation is indicated by the 'division' symbol.

It also may be indicated by using a 'slash' symbol or a horizontal line.

Suppose we have the expression "thirty-six divided by nine."

To what does this expression evaluate? Click the “Submit” button after entering your answer.

The answer to a division operation is known as the |B| quotient |/B| . In this case: <EQUATION>.

Division and multiplication are inverse operations. We can evaluate the previous expression by multiplying thirty-six times the reciprocal of nine.

Whenever we multiply two real numbers, the result is always a real number. This is known as the |B| closure property of multiplication |/B| . Here, we have: <EQUATION>

Another type of operation involves the taking of a number to a power. For example: <EQUATION>

This means that we multiply the number times itself, the number of times given by the power.

To what does our power expression evaluate? Click the “Submit” button after entering your answer.

The power number is known as the exponent. The number that is taken to a power is known as the base. We will learn more about operations with exponents in future lessons.

Sometimes an expression contains more than one operation, such as: <EQUATION>. The evaluation of the expression can depend on the order in which the operations are performed.

In order to properly evaluate an expression with multiple operations, we must follow a rule called the order of operations.

The first thing we do is to perform all operations inside grouping symbols, such as parentheses or brackets, and braces, or as indicated by fraction bars.

When evaluating expressions, we first evaluate all powers.

Next, we perform all multiplications and divisions, going from left to right.

Finally, we perform all additions and subtractions, going from left to right.

Now, let's use an example to illustrate the proper use of our order of operations rule.

Mark needs to go to the store to buy some new shoes. You must direct him on each leg of his trip by correctly evaluating the given expression and entering the answer into the box.

When you are finished evaluating all legs of the journey, click the "Go" button to show the path you have calculated for him.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education