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:

1) \(|-7 + -2|-4\)

Step1: Simplify inside the absolute value

\(-7+(-2)=-9\), so \(|-9| = 9\)

Step2: Subtract 4

\(9 - 4=5\)

2) \(|1 - 2|+4\)

Step1: Simplify inside the absolute value

\(1-2=-1\), so \(|-1| = 1\)

Step2: Add 4

\(1 + 4=5\)

3) \(|6 - 9|-3\)

Step1: Simplify inside the absolute value

\(6 - 9=-3\), so \(|-3| = 3\)

Step2: Subtract 3

\(3-3 = 0\)

4) \(|9 + 1|+|-8 + 4|\)

Step1: Simplify inside each absolute value

\(9 + 1=10\), so \(|10| = 10\); \(-8 + 4=-4\), so \(|-4| = 4\)

Step2: Add the results

\(10+4 = 14\)

5) \(|1 - 9|+|5 + 4|\)

Step1: Simplify inside each absolute value

\(1-9=-8\), so \(|-8| = 8\); \(5 + 4=9\), so \(|9| = 9\)

Step2: Add the results

\(8+9 = 17\)

6) \(|6 - 8|+|5 + 3|\)

Step1: Simplify inside each absolute value

\(6-8=-2\), so \(|-2| = 2\); \(5 + 3=8\), so \(|8| = 8\)

Step2: Add the results

\(2+8 = 10\)

7) \(\frac{|5 - 9|}{|1 + 1|}\)

Step1: Simplify inside each absolute value

\(5-9=-4\), so \(|-4| = 4\); \(1 + 1=2\), so \(|2| = 2\)

Step2: Divide the results

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

8) \(\frac{|8 - 5|}{|-2 + 1|}+4\)

Step1: Simplify inside each absolute value

\(8-5 = 3\), so \(|3| = 3\); \(-2+1=-1\), so \(|-1| = 1\)

Step2: Divide and then add 4

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

9) \(\frac{|6 + 2|}{|5 - 1|}-2\)

Step1: Simplify inside each absolute value

\(6+2 = 8\), so \(|8| = 8\); \(5-1 = 4\), so \(|4| = 4\)

Step2: Divide and then subtract 2

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

10) \(10+|1 - 8|+6\)

Step1: Simplify inside the absolute value

\(1-8=-7\), so \(|-7| = 7\)

Step2: Add all the numbers

\(10+7+6=23\)

11) \(2+|-6 + -2|+4\)

Step1: Simplify inside the absolute value

\(-6+(-2)=-8\), so \(|-8| = 8\)

Step2: Add all the numbers

\(2+8+4=14\)

12) \(12+|6 - 2|+4\)

Step1: Simplify inside the absolute value

\(6-2 = 4\), so \(|4| = 4\)

Step2: Add all the numbers

\(12+4+4=20\)

13) \(\frac{|7 - 15|}{|1 - 9|}+|-11|\)

Step1: Simplify inside each absolute value

\(7-15=-8\), so \(|-8| = 8\); \(1-9=-8\), so \(|-8| = 8\); \(|-11| = 11\)

Step2: Divide and then add

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

14) \(|6 - 6|+|5 - 5|+10\)

Step1: Simplify inside each absolute value

\(6-6 = 0\), so \(|0| = 0\); \(5-5 = 0\), so \(|0| = 0\)

Step2: Add all the numbers

\(0+0+10=10\)

15) \(\frac{-8}{|-7 + -1|}+4\)

Step1: Simplify inside the absolute value

\(-7+(-1)=-8\), so \(|-8| = 8\)

Step2: Divide and then add 4

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

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. \(3\)