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Study Guides > Prealgebra

Notation and Modeling Multiplication of Whole Numbers

Learning Outcomes

  • Use symbols and words to represent multiplication
  • Model multiplication of whole numbers
 

Use Multiplication Notation

Suppose you were asked to count all these pennies shown below. 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 [latex]3[/latex] times.

[latex]8+8+8[/latex]

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

[latex]3\times 8[/latex]

We call each number being multiplied a factor and the result the product. We read [latex]3\times 8[/latex] 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 [latex]\times [/latex] as well as the dot, [latex]\cdot [/latex] , and parentheses [latex]\left(\right)[/latex]

Operation Symbols for Multiplication

To describe multiplication, we can use symbols and words.
Operation Notation Expression Read as Result
[latex]\text{Multiplication}[/latex] [latex]\times [/latex] [latex-display]\cdot [/latex-display] [latex]\left(\right)[/latex] [latex]3\times 8[/latex] [latex-display]3\cdot 8[/latex-display] [latex]3\left(8\right)[/latex] [latex]\text{three times eight}[/latex] [latex]\text{the product of 3 and 8}[/latex]
 

example

Translate from math notation to words:
  1. [latex]7\times 6[/latex]
  2. [latex]12\cdot 14[/latex]
  3. [latex]6\left(13\right)[/latex]
Solution
  • We read this as seven times six and the result is the product of seven and six.
  • We read this as twelve times fourteen and the result is the product of twelve and fourteen.
  • We read this as six times thirteen and the result is the product of six and thirteen.
    In the video below we present more ways that multiplication is expressed with words, and how to translate the words to math notation. https://youtu.be/KavmzEwvh1g  

Model Multiplication of Whole Numbers

There are many ways to model multiplication. Unlike in the previous sections where we used [latex]\text{base - 10}[/latex] 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.

example

Model: [latex]3\times 8[/latex].

Answer: Solution To model the product [latex]3\times 8[/latex], we’ll start with a row of [latex]8[/latex] counters. An image of a horizontal row of 8 counters. The other factor is [latex]3[/latex], so we’ll make [latex]3[/latex] rows of [latex]8[/latex] counters. An image of 3 horizontal rows of counters, each row containing 8 counters. Now we can count the result. There are [latex]24[/latex] counters in all. [latex-display]3\times 8=24[/latex-display] If you look at the counters sideways, you’ll see that we could have also made [latex]8[/latex] rows of [latex]3[/latex] counters. The product would have been the same. We’ll get back to this idea later.

 

try it

Model each multiplication: [latex]4\times 6[/latex].

Answer: No Alt Text

  Model each multiplication: [latex]5\times 7[/latex].

Answer: No Alt Text

 

Licenses & Attributions

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CC licensed content, Shared previously

  • The Language of Multiplication. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Question ID: 144396. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

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