example
Simplify:
[latex-display]|3|[/latex-display]
[latex-display]|-44|[/latex-display]
[latex-display]|0|[/latex-display]
Solution:
1. |
|
|
[latex]|3|[/latex] |
[latex]3[/latex] is [latex]3[/latex] units from zero. |
[latex]3[/latex] |
2. |
|
|
[latex]|-44|[/latex] |
[latex]−44[/latex] is [latex]44[/latex] units from zero. |
[latex]44[/latex] |
3. |
|
|
[latex]|0|[/latex] |
[latex]0[/latex] is already at zero. |
[latex]0[/latex] |
In the video below we show more example of how to find the absolute value of an integer.
https://youtu.be/I8bTqGmkqGI
We treat absolute value bars just like we treat parentheses in the order of operations. We simplify the expression inside first.
example
Fill in [latex]\text{<},\text{>},\text{or}=[/latex] for each of the following:
- [latex]|-5|___-|-5|[/latex]
- [latex]8___-|-8|[/latex]
- [latex]-9___-|-9|[/latex]
- [latex]-|-7|___ - 7[/latex]
Answer:
Solution:
To compare two expressions, simplify each one first. Then compare.
1. |
|
|
[latex]|-5|___-|-5|[/latex] |
Simplify. |
[latex]5___ - 5[/latex] |
Order. |
[latex]5>-5[/latex] |
2. |
|
|
[latex]8___-|-8|[/latex] |
Simplify. |
[latex]8___ - 8[/latex] |
Order. |
[latex]8>-8[/latex] |
3. |
|
|
[latex]-9___-|-9|[/latex] |
Simplify. |
[latex]-9___ - 9[/latex] |
Order. |
[latex]-9=-9[/latex] |
4. |
|
|
[latex]-|-7|___ - 7[/latex] |
Simplify. |
[latex]-7___ - 7[/latex] |
Order. |
[latex]-7=-7[/latex] |
In the video below we show more examples of how to compare expressions that include absolute value and integers.
https://youtu.be/TendEcSaM3w
Absolute value bars act like grouping symbols. First simplify inside the absolute value bars as much as possible. Then take the absolute value of the resulting number, and continue with any operations outside the absolute value symbols.
example
Simplify:
- [latex]|9 - 3|[/latex]
- [latex]4|-2|[/latex]
Answer:
Solution:
For each expression, follow the order of operations. Begin inside the absolute value symbols just as with parentheses.
1. |
|
|
[latex]|9−3|[/latex] |
Simplify inside the absolute value sign. |
[latex]|6|[/latex] |
Take the absolute value. |
[latex]6[/latex] |
2. |
|
|
[latex]4|−2|[/latex] |
Take the absolute value. |
[latex]4⋅2[/latex] |
Multiply. |
[latex]8[/latex] |
example
Simplify: [latex]|8+7|-|5+6|[/latex].
Answer:
Solution:
For each expression, follow the order of operations. Begin inside the absolute value symbols just as with parentheses.
|
[latex]|8+7|−|5+6|[/latex] |
Simplify inside each absolute value sign. |
[latex]|15|−|11|[/latex] |
Subtract. |
[latex]4[/latex] |
example
Simplify: [latex]24-|19 - 3\left(6 - 2\right)|[/latex].
Answer:
Solution:
We use the order of operations. Remember to simplify grouping symbols first, so parentheses inside absolute value symbols would be first.
|
[latex]24-|19 - 3\left(6 - 2\right)|[/latex] |
Simplify in the parentheses first. |
[latex]24-|19 - 3\left(4\right)|[/latex] |
Multiply [latex]3\left(4\right)[/latex] . |
[latex]24-|19 - 12|[/latex] |
Subtract inside the absolute value sign. |
[latex]24-|7|[/latex] |
Take the absolute value. |
[latex]24 - 7[/latex] |
Subtract. |
[latex]17[/latex] |