# Whole Numbers

## Multiply Whole Numbers


### Use Multiplication Notation

Suppose you were asked to count all these pennies shown in .
Would you count the pennies individually? Or would you count the number of pennies in each row and add that number  times.
Multiplication is a way to represent repeated addition. So instead of adding  three times, we could write a multiplication expression.
We call each number being multiplied a factor and the result the product. We read  as three times eight, and the result as the product of three and eight.
There are several symbols that represent multiplication. These include the symbol  as well as the dot, , and parentheses 

### Model Multiplication of Whole Numbers

There are many ways to model multiplication. Unlike in the previous sections where we used  blocks, here we will use counters to help us understand the meaning of multiplication. A counter is any object that can be used for counting. We will use round blue counters.

### Multiply Whole Numbers

In order to multiply without using models, you need to know all the one digit multiplication facts. Make sure you know them fluently before proceeding in this section.
 shows the multiplication facts. Each box shows the product of the number down the left column and the number across the top row. If you are unsure about a product, model it. It is important that you memorize any number facts you do not already know so you will be ready to multiply larger numbers.
What happens when you multiply a number by zero? You can see that the product of any number and zero is zero. This is called the Multiplication Property of Zero.
What happens when you multiply a number by one? Multiplying a number by one does not change its value. We call this fact the Identity Property of Multiplication, and  is called the multiplicative identity.
Earlier in this chapter, we learned that the Commutative Property of Addition states that changing the order of addition does not change the sum. We saw that  is the same as 
Is this also true for multiplication? Let’s look at a few pairs of factors.
When the order of the factors is reversed, the product does not change. This is called the Commutative Property of Multiplication.
To multiply numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition and subtraction.
We start by multiplying  by 
We write the  in the ones place of the product. We carry the  tens by writing  above the tens place.
Then we multiply the  by the  and add the  above the tens place to the product. So  and  Write the  in the tens place of the product.
The product is 
When we multiply two numbers with a different number of digits, it’s usually easier to write the smaller number on the bottom. You could write it the other way, too, but this way is easier to work with.
When we multiply by a number with two or more digits, we multiply by each of the digits separately, working from right to left. Each separate product of the digits is called a partial product. When we write partial products, we must make sure to line up the place values.
When there are three or more factors, we multiply the first two and then multiply their product by the next factor. For example:


### Translate Word Phrases to Math Notation

Earlier in this section, we translated math notation into words. Now we’ll reverse the process and translate word phrases into math notation. Some of the words that indicate multiplication are given in .

### Multiply Whole Numbers in Applications

We will use the same strategy we used previously to solve applications of multiplication. First, we need to determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify to get the answer. Finally, we write a sentence to answer the question.
If we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area. The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.
For a rectangular figure, the area is the product of the length and the width.  shows a rectangular rug with a length of  feet and a width of  feet. Each square is  foot wide by  foot long, or  square foot. The rug is made of  squares. The area of the rug is  square feet.

### Key Concepts

1. Multiplication Property of Zero

2. Identity Property of Multiplication

3. Commutative Property of Multiplication

4. Multiply two whole numbers to find the product.


### Practice Makes Perfect

Use Multiplication Notation 
In the following exercises, translate from math notation to words.
Model Multiplication of Whole Numbers 
In the following exercises, model the multiplication.
Multiply Whole Numbers 
In the following exercises, fill in the missing values in each chart.
In the following exercises, multiply.
Translate Word Phrases to Math Notation 
In the following exercises, translate and simplify.
Mixed Practice 
In the following exercises, simplify.
In the following exercises, translate and simplify.
Multiply Whole Numbers in Applications 
In the following exercises, solve.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?
