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By the end of this section, you will be able to:
  • Use multiplication notation
  • Model multiplication of whole numbers
  • Multiply whole numbers
  • Translate word phrases to math notation
  • Multiply whole numbers in applications

Before you get started, take this readiness quiz.

  1. Add: 1,683 + 479 .
    If you missed this problem, review Add Whole Numbers .
  2. Subtract: 605 321 .
    If you missed this problem, review Subtract Whole Numbers .

Use multiplication notation

Suppose you were asked to count all these pennies shown in [link] .

An image of 3 horizontal rows of pennies, each row containing 8 pennies.

Would you count the pennies individually? Or would you count the number of pennies in each row and add that number 3 times.

8 + 8 + 8

Multiplication is a way to represent repeated addition. So instead of adding 8 three times, we could write a multiplication expression.

3 × 8

We call each number being multiplied a factor and the result the product    . We read 3 × 8 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 ( ).

Operation symbols for multiplication

To describe multiplication, we can use symbols and words.

Operation Notation Expression Read as Result
Multiplication ×
·
( )
3 × 8
3 · 8
3 ( 8 )
three times eight the product of 3 and 8

Translate from math notation to words:

  1. 7 × 6
  2. 12 · 14
  3. 6 ( 13 )

Solution

  • We read this as seven times six or the product of seven and six .
  • We read this as twelve times fourteen or the product of twelve and fourteen .
  • We read this as six times thirteen or the product of six and thirteen .
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Translate from math notation to words:

  1. 8 × 7
  2. 18 · 11
  1. eight times seven ; the product of eight and seven
  2. eighteen times eleven ; the product of eighteen and eleven
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Translate from math notation to words:

  1. ( 13 ) ( 7 )
  2. 5 ( 16 )
  1. thirteen times seven ; the product of thirteen and seven
  2. five times sixteen; the product of five and sixteen
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Model multiplication of whole numbers

There are many ways to model multiplication. Unlike in the previous sections where we used base-10 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.

Model: 3 × 8 .

Solution

To model the product 3 × 8 , we’ll start with a row of 8 counters.
An image of a horizontal row of 8 counters.

The other factor is 3 , so we’ll make 3 rows of 8 counters.
An image of 3 horizontal rows of counters, each row containing 8 counters.

Now we can count the result. There are 24 counters in all.

3 × 8 = 24

If you look at the counters sideways, you’ll see that we could have also made 8 rows of 3 counters. The product would have been the same. We’ll get back to this idea later.

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Model each multiplication: 4 × 6 .


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Model each multiplication: 5 × 7 .


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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.

[link] 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.

Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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