Summary: Multiplying Whole Numbers

Key Concepts

Operation	Notation	Expression	Read as	Result
Multiplication	[latex]\times [/latex] [latex]\cdot [/latex] [latex]\left(\right)[/latex]	[latex]3\times 8[/latex] [latex]3\cdot 8[/latex] [latex]3\left(8\right)[/latex]	three times eight	the product of [latex]3[/latex] and [latex]8[/latex]

Operation

Notation

Expression

Read as

Result

Multiplication

[latex]\times [/latex]

[latex]\cdot [/latex]

[latex]\left(\right)[/latex]

[latex]3\times 8[/latex]

[latex]3\cdot 8[/latex]

[latex]3\left(8\right)[/latex]

three times eight

the product of [latex]3[/latex] and [latex]8[/latex]

Multiplication Property of Zero
- The product of any number and [latex]0[/latex] is [latex]0[/latex]

[latex]a\cdot 0=0[/latex]

[latex]0\cdot a=0[/latex]

Identity Property of Multiplication
- The product of any number and [latex]1 [/latex] is the number

[latex]1\cdot a=a[/latex]

[latex]a\cdot 1=a[/latex]

Commutative Property of Multiplication
- Changing the order of the factors does not change their product.

[latex]a\cdot b=b\cdot a[/latex]

Multiply two whole numbers to find the product.
1. Write the numbers so each place value lines up vertically.
2. Multiply the digits in each place value.
3. Work from right to left, starting with the ones place in the bottom number.
4. Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
5. If a product in a place value is more than 9, carry to the next place value.
6. Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
7. Insert a zero as a placeholder with each additional partial product.
8. Add the partial products.