Division of Signed Numbers
The sign of the quotient of two numbers depends on their signs.
Same signs |
Quotient |
•Two positives
•Two negatives |
Positive
Positive |
Different signs |
Quotient |
•Positive & negative
•Negative & positive |
Negative
Negative |
Remember, you can always check the answer to a division problem by multiplying.
example
Divide each of the following:
- [latex]-27\div 3[/latex]
- [latex]-100\div \left(-4\right)[/latex]
Solution
1. |
|
|
[latex]-27\div 3[/latex] |
Divide, noting that the signs are different and so the quotient is negative. |
[latex]-9[/latex] |
2. |
|
|
[latex]-100\div \left(-4\right)[/latex] |
Divide, noting that the signs are the same and so the quotient is positive. |
[latex]25[/latex] |
example
Divide each of the following:
- [latex]16\div \left(-1\right)[/latex]
- [latex]-20\div \left(-1\right)[/latex]
Answer:
Solution
1. |
|
|
[latex]16\div \left(-1\right)[/latex] |
The dividend, [latex]16[/latex], is being divided by [latex]–1.[/latex] |
[latex]-16[/latex] |
Dividing a number by [latex]–1[/latex] gives its opposite. |
|
Notice that the signs were different, so the result was negative. |
|
2. |
|
|
[latex]-20\div \left(-1\right)[/latex] |
The dividend, [latex]–20[/latex], is being divided by [latex]–1.[/latex] |
[latex]20[/latex] |
Dividing a number by [latex]–1[/latex] gives its opposite. |
|
Notice that the signs were the same, so the quotient was positive.