Summary: Dividing Whole Numbers

Key Concepts

Operation	Notation	Expression	Read as	Result
[latex]\text{Division}[/latex]	[latex]\div [/latex] [latex]\frac{a}{b}[/latex] [latex]b\overline{)a}[/latex] [latex]a/b[/latex]	[latex]12\div 4[/latex] [latex]\frac{12}{4}[/latex] [latex]4\overline{)12}[/latex] [latex]12/4[/latex]	[latex]\text{Twelve divided by four}[/latex]	[latex]\text{the quotient of 12 and 4}[/latex]

Operation

Notation

Expression

Read as

Result

[latex]\text{Division}[/latex]

[latex]\div [/latex]

[latex]\frac{a}{b}[/latex]

[latex]b\overline{)a}[/latex]

[latex]a/b[/latex]

[latex]12\div 4[/latex]

[latex]\frac{12}{4}[/latex]

[latex]4\overline{)12}[/latex]

[latex]12/4[/latex]

[latex]\text{Twelve divided by four}[/latex]

[latex]\text{the quotient of 12 and 4}[/latex]

Division Properties of One
- Any number (except [latex]0[/latex]) divided by itself is one.

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

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

Division Properties of Zero
- Zero divided by any number is [latex]0[/latex].

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

[latex]a\div 0[/latex] undefined

Divide whole numbers.
1. Divide the first digit of the dividend by the divisor. If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on.
2. Write the quotient above the dividend.
3. Multiply the quotient by the divisor and write the product under the dividend.
4. Subtract that product from the dividend.
5. Bring down the next digit of the dividend.
6. Repeat from Step [latex]1[/latex] until there are no more digits in the dividend to bring down.
7. Check by multiplying the quotient times the divisor.

dividend: When dividing two numbers, the dividend is the number being divided.

divisor: When dividing two numbers, the divisor is the number dividing the dividend.