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.
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:- [latex]7\times 6[/latex]
- [latex]12\cdot 14[/latex]
- [latex]6\left(13\right)[/latex]
- 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.
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.
The other factor is [latex]3[/latex], so we’ll make [latex]3[/latex] rows of [latex]8[/latex] 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: 
Answer:
Licenses & Attributions
CC licensed content, Original
- Question ID 144396. Authored by: Lumen Learning. License: CC BY: Attribution.
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.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].
