Math worksheet for evaluating absolute value expressions, featuring 10 problems with absolute value notation and operations.

Let’s solve each problem step by step. Remember: absolute value means “distance from zero,” so it’s always positive (or zero). We do the math inside the absolute value bars first, then take the absolute value, then do any multiplication/division/addition/subtraction outside.

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1)
Expression: `| -8 - 4 | / ( | -3 | × 2 )`

Step 1: Inside top absolute value: -8 - 4 = -12 → | -12 | = 12
Step 2: Bottom: | -3 | = 3 → 3 × 2 = 6
Step 3: 12 ÷ 6 = 2

✔ Answer: 2

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2)
Expression: `| -5 + 6 | + ( | -9 | / | -3 | ) × 7`

Step 1: | -5 + 6 | = | 1 | = 1
Step 2: | -9 | = 9, | -3 | = 3 → 9 ÷ 3 = 3
Step 3: 3 × 7 = 21
Step 4: 1 + 21 = 22

✔ Answer: 22

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3)
Expression: `| -17 + 46 | + | -15 | × 11`

Step 1: -17 + 46 = 29 → |29| = 29
Step 2: | -15 | = 15 → 15 × 11 = 165
Step 3: 29 + 165 = 194

✔ Answer: 194

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4)
Expression: `| -10 × 20 | + | -18 | / | -6 |`

Step 1: -10 × 20 = -200 → | -200 | = 200
Step 2: | -18 | = 18, | -6 | = 6 → 18 ÷ 6 = 3
Step 3: 200 + 3 = 203

✔ Answer: 203

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5)
Expression: `| -16 - 29 | - | -4 × 14 |`

Step 1: -16 - 29 = -45 → | -45 | = 45
Step 2: -4 × 14 = -56 → | -56 | = 56
Step 3: 45 - 56 = -11

✔ Answer: -11

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6)
Expression: `| -25 + 28 | - | -30 + 23 |`

Step 1: -25 + 28 = 3 → |3| = 3
Step 2: -30 + 23 = -7 → | -7 | = 7
Step 3: 3 - 7 = -4

✔ Answer: -4

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7)
Expression: `| -11 | × 8 - | -50 | / | -5 |`

Step 1: | -11 | = 11 → 11 × 8 = 88
Step 2: | -50 | = 50, | -5 | = 5 → 50 ÷ 5 = 10
Step 3: 88 - 10 = 78

✔ Answer: 78

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8)
Expression: `| -42 - 24 | - | -21 - 31 | / (13 × 4)`

Step 1: -42 - 24 = -66 → | -66 | = 66
Step 2: -21 - 31 = -52 → | -52 | = 52
Step 3: 13 × 4 = 52 → 52 ÷ 52 = 1
Step 4: 66 - 1 = 65

✔ Answer: 65

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9)
Expression: `( |3 - 30| / (36 - 27) ) × ( | -13 - 21 | / (19 - 2) )`

Break into two parts:

Part A: |3 - 30| = | -27 | = 27; denominator: 36 - 27 = 9 → 27 ÷ 9 = 3
Part B: | -13 - 21 | = | -34 | = 34; denominator: 19 - 2 = 17 → 34 ÷ 17 = 2
Multiply: 3 × 2 = 6

✔ Answer: 6

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10)
Expression: `| -49 | - | -9 | - 39 / | -3 |`

Step 1: | -49 | = 49
Step 2: | -9 | = 9
Step 3: | -3 | = 3 → 39 ÷ 3 = 13
Step 4: 49 - 9 - 13 = 40 - 13 = 27

✔ Answer: 27

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Final Answer:
1) 2
2) 22
3) 194
4) 203
5) -11
6) -4
7) 78
8) 65
9) 6
10) 27