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

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

    • Any number divided by one is the same number.

[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]

    • Dividing a number by zero is undefined.

[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.

Glossary

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.
quotient
The quotient is the result of dividing two numbers.