Question

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: ( |7 - 8|+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. ( |-7 + -2|-4 = )____ 2) ( |1 - 2|+4 = )__ 3) ( |6 - 9|-3 = )____
2. ( |9 + 1|+|-8 + 4| = )____ 5) ( |1 - 9|+|5 + 4| = )__ 6) ( |6 - 8|+|5 + 3| = )____
3. ( \frac{|5 - 9|}{|1 + 1|} = )____ 8) ( \frac{|8 - 5|}{|-2 + 1|}+4 = )__ 9) ( \frac{|6 + 2|}{|5 - 1|}-2 = )____
4. ( 10+|1 - 8|+6 = )____ 11) ( 2+|-6 + -2|+4 = )__ 12) ( 12+|6 - 2|+4 = )____
5. ( \frac{|7 - 15|}{|1 - 9|}+|-11| = )____ 14) ( |6 - 6|+|5 - 5|+10 = )__ 15) ( \frac{-8}{|-7 + -1|}+4 = )____

Explanation:

Step1: Simplify inside absolute value

For \(|-7 + - 2|-4\), first calculate \(-7+(-2)=-9\). Then \(|-9| = 9\).

Step2: Do subtraction

\(9 - 4=5\)

Step1: Simplify inside absolute value

For \(|1 - 2|+4\), calculate \(1 - 2=-1\). Then \(|-1| = 1\).

Step2: Do addition

\(1+4 = 5\)

Step1: Simplify inside absolute value

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

Step2: Do subtraction

\(3-3 = 0\)

Step1: Simplify inside absolute values

For \(|9 + 1|+|-8 + 4|\), calculate \(9 + 1 = 10\) and \(-8+4=-4\). Then \(|10| = 10\) and \(|-4| = 4\).

Step2: Do addition

\(10 + 4=14\)

Step1: Simplify inside absolute values

For \(|1 - 9|+|5 + 4|\), calculate \(1 - 9=-8\) and \(5 + 4 = 9\). Then \(|-8| = 8\) and \(|9| = 9\).

Step2: Do addition

\(8+9 = 17\)

Step1: Simplify inside absolute values

For \(|6 - 8|+|5 + 3|\), calculate \(6 - 8=-2\) and \(5 + 3 = 8\). Then \(|-2| = 2\) and \(|8| = 8\).

Step2: Do addition

\(2+8 = 10\)

Step1: Simplify inside absolute values

For \(\frac{|5 - 9|}{|1 + 1|}\), calculate \(5 - 9=-4\) and \(1 + 1 = 2\). Then \(|-4| = 4\) and \(|2| = 2\).

Step2: Do division

\(\frac{4}{2}=2\)

Step1: Simplify inside absolute values

For \(\frac{|8 - 5|}{|-2 + 1|}+4\), calculate \(8 - 5 = 3\) and \(-2+1=-1\). Then \(|3| = 3\) and \(|-1| = 1\).

Step2: Do division and addition

\(\frac{3}{1}+4=3 + 4=7\)

Step1: Simplify inside absolute values

For \(\frac{|6 + 2|}{|5 - 1|}-2\), calculate \(6 + 2 = 8\) and \(5 - 1 = 4\). Then \(|8| = 8\) and \(|4| = 4\).

Step2: Do division and subtraction

\(\frac{8}{4}-2=2 - 2=0\)

Step1: Simplify inside absolute value

For \(10+|1 - 8|+6\), calculate \(1 - 8=-7\). Then \(|-7| = 7\).

Step2: Do addition

\(10+7+6=23\)

Step1: Simplify inside absolute value

For \(2+|-6 + -2|+4\), calculate \(-6+(-2)=-8\). Then \(|-8| = 8\).

Step2: Do addition

\(2 + 8+4=14\)

Step1: Simplify inside absolute value

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

Step2: Do addition

\(12+4+4=20\)

Step1: Simplify inside absolute values

For \(\frac{|7 - 15|}{|1 - 9|}+|-11|\), calculate \(7 - 15=-8\) and \(1 - 9=-8\). Then \(|-8| = 8\) and \(|-11| = 11\).

Step2: Do division and addition

\(\frac{8}{8}+11=1 + 11=12\)

Step1: Simplify inside absolute values

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

Step2: Do addition

\(0+0+10=10\)

Step1: Simplify inside absolute value

For \(\frac{-8}{|-7 + -1|}+4\), calculate \(-7+(-1)=-8\). Then \(|-8| = 8\).

Step2: Do division and addition

\(\frac{-8}{8}+4=-1 + 4=3\)

Answer:

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