Question

simplifying expressions with
directions: simplify each of the expressions below. according to the correct order of operations, you should treat
absolute value like an expression in parentheses. that means, simplify the absolute value expression first, before you
add or subtract any numbers outside of the absolute value symbol.
examples: |8 - 7| + 3 =? |5 - 7| + |10 + 1| =? \\( \frac { | 8 + 2 | } { | 6 - 1 | } + 7 =? \\)

1

+ 3 =?

-2

+

11

=? \\( \frac { 10 } { 5 } + 7 =? \\)

1 + 3 = 4 2 + 11 = 13 2 + 7 = 9

1. |4 + 2| - 4 = ____ 2) |8 + 2| + 4 = __ 3) |9 - 6| - 2 = ____
2. |9 + 3| + |8 + 3| = ____ 5) |9 - 5| + |5 + 4| = __ 6) |8 - 4| - |5 - 1| = ____
3. |9 + 5| + |1 + 3| = ____ 8) |9 + 3| + |8 + 3| - 6 = __ 9) 8 + |9 + 3| + |8 + 3| = ____
4. 10 + |1 + 3| + 6 = ____ 11) 8 - |2 + 2| - 4 = __ 12) |12| + |6 - 2| - 4 = ____
5. |7 - 1| - |3 + 2| = ____ 14) |6 - 6| - |5 - 5| + 10 = __ 15) |5 - 5 + 3| + 5 - |2| = ____

Explanation:

Step1: Calculate inside the absolute value

For \(|4 + 2|-4\), first calculate \(4+2 = 6\).

Step2: Apply the absolute value

\(|6|=6\).

Step3: Do the subtraction

\(6-4 = 2\).

Step1: Calculate inside the absolute value

For \(|8 + 2|+4\), first calculate \(8 + 2=10\).

Step2: Apply the absolute value

\(|10| = 10\).

Step3: Do the addition

\(10+4=14\).

Step1: Calculate inside the absolute value

For \(|9 - 6|-2\), first calculate \(9-6 = 3\).

Step2: Apply the absolute value

\(|3|=3\).

Step3: Do the subtraction

\(3-2 = 1\).

Step1: Calculate inside the absolute values

For \(|9 + 3|+|8 + 3|\), calculate \(9+3 = 12\) and \(8+3=11\).

Step2: Apply the absolute values

\(|12| = 12\) and \(|11|=11\).

Step3: Do the addition

\(12 + 11=23\).

Step1: Calculate inside the absolute values

For \(|9 - 5|+|5 + 4|\), calculate \(9-5 = 4\) and \(5+4 = 9\).

Step2: Apply the absolute values

\(|4|=4\) and \(|9| = 9\).

Step3: Do the addition

\(4+9=13\).

Step1: Calculate inside the absolute values

For \(|8 - 4|-|5 - 1|\), calculate \(8-4 = 4\) and \(5-1=4\).

Step2: Apply the absolute values

\(|4|=4\) and \(|4| = 4\).

Step3: Do the subtraction

\(4-4=0\).

Step1: Calculate inside the absolute values

For \(|9 + 5|+|1 + 3|\), calculate \(9+5 = 14\) and \(1+3=4\).

Step2: Apply the absolute values

\(|14| = 14\) and \(|4|=4\).

Step3: Do the addition

\(14+4=18\).

Step1: Calculate inside the absolute values

For \(|9 + 3|+|8 + 3|-6\), calculate \(9+3 = 12\) and \(8+3=11\).

Step2: Apply the absolute values

\(|12| = 12\) and \(|11|=11\).

Step3: Do the addition and subtraction

\(12+11-6=17\).

Step1: Calculate inside the absolute values

For \(8+|9 + 3|+|8 + 3|\), calculate \(9+3 = 12\) and \(8+3=11\).

Step2: Apply the absolute values

\(|12| = 12\) and \(|11|=11\).

Step3: Do the addition

\(8+12+11=31\).

Step1: Calculate inside the absolute value

For \(10+|1 + 3|+6\), calculate \(1+3 = 4\).

Step2: Apply the absolute value

\(|4|=4\).

Step3: Do the addition

\(10+4+6=20\).

Step1: Calculate inside the absolute value

For \(8-|2 + 2|-4\), calculate \(2+2 = 4\).

Step2: Apply the absolute value

\(|4|=4\).

Step3: Do the subtraction

\(8-4-4=0\).

Step1: Calculate inside the absolute value

For \(|12|+|6 - 2|-4\), calculate \(6-2 = 4\).

Step2: Apply the absolute values

\(|12| = 12\) and \(|4|=4\).

Step3: Do the addition and subtraction

\(12+4-4=12\).

Step1: Calculate inside the absolute values

For \(|7 - 1|-|3 + 2|\), calculate \(7-1 = 6\) and \(3+2=5\).

Step2: Apply the absolute values

\(|6|=6\) and \(|5| = 5\).

Step3: Do the subtraction

\(6-5=1\).

Step1: Calculate inside the absolute values

For \(|6 - 6|-|5 - 5|+10\), calculate \(6-6 = 0\) and \(5-5=0\).

Step2: Apply the absolute values

\(|0|=0\) and \(|0| = 0\).

Step3: Do the addition and subtraction

\(0-0+10=10\).

Step1: Calculate inside the absolute value

For \(|5 - 5+3|+5-|2|\), first calculate \(5-5+3=3\).

Step2: Apply the absolute values

\(|3|=3\) and \(|2| = 2\).

Step3: Do the addition and subtraction

\(3+5-2=6\).

Answer:

1. \(2\)
2. \(14\)
3. \(1\)
4. \(23\)
5. \(13\)
6. \(0\)
7. \(18\)
8. \(17\)
9. \(31\)
10. \(20\)
11. \(0\)
12. \(12\)
13. \(1\)
14. \(10\)
15. \(6\)