Evaluate Each Expression Using The Order Of Operations

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Evaluate Each Expression Using The Order Of Operations. 1. 17-5-4+2 2. 40-32+8 +5-2 3.35- 14 +2+8 4. (4-7) -6-7+ 20 92 -13 5. 218-(5+3′)+7] 6.[(-5+1)+2]-1-71 32 -15 6(2 + 4)-1 7.1+(-2-5)’ +(14-17)-4 8. 2-3+1 88 2 +8+3 9. 17-5-3-5 10. 4+3 3 +1 13+7 +7 (3-4) 11. 12.

The Correct Answer and Explanation is :

To solve these expressions, we need to follow the Order of Operations: PEMDAS/BODMAS:

  1. P/B: Parentheses/Brackets
  2. E/O: Exponents/Orders (powers and roots)
  3. MD: Multiplication and Division (left to right)
  4. AS: Addition and Subtraction (left to right)

Let’s evaluate the given expressions step-by-step:

1. ( 17 – 5 – 4 + 2 )

Solution:
Evaluate left to right:
( 17 – 5 = 12 ), ( 12 – 4 = 8 ), ( 8 + 2 = 10 ).
Answer: 10

2. ( 40 – 32 + 8 + 5 – 2 )

Solution:
Evaluate left to right:
( 40 – 32 = 8 ), ( 8 + 8 = 16 ), ( 16 + 5 = 21 ), ( 21 – 2 = 19 ).
Answer: 19

3. ( 35 – 14 + 2 + 8 )

Solution:
Evaluate left to right:
( 35 – 14 = 21 ), ( 21 + 2 = 23 ), ( 23 + 8 = 31 ).
Answer: 31

4. ( (4 – 7) – 6 – 7 + 20 – 92 – 13 )

Solution:

  1. Parentheses: ( 4 – 7 = -3 ).
  2. Evaluate left to right:
    [ -3 – 6 = -9, -9 – 7 = -16, -16 + 20 = 4, 4 – 92 = -88, -88 – 13 = -101 ].
    Answer: -101

5. ( 218 – (5 + 3) + 7 )

Solution:

  1. Parentheses: ( 5 + 3 = 8 ).
  2. Subtraction and addition:
    [ 218 – 8 = 210, 210 + 7 = 217 ].
    Answer: 217

6. ( [(-5 + 1) + 2] – 1 – 71 )

Solution:

  1. Inside brackets: ( -5 + 1 = -4 ), then ( -4 + 2 = -2 ).
  2. Evaluate outside:
    [ -2 – 1 = -3, -3 – 71 = -74 ].
    Answer: -74

7. ( 1 + (-2 – 5) + (14 – 17) – 4 )

Solution:

  1. Parentheses: ( -2 – 5 = -7 ), ( 14 – 17 = -3 ).
  2. Combine terms:
    [ 1 – 7 – 3 – 4 = -13 ].
    Answer: -13

8. ( 2 – 3 + 1 – 88 + 2 + 8 + 3 )

Solution:
Evaluate left to right:
( 2 – 3 = -1 ), ( -1 + 1 = 0 ), ( 0 – 88 = -88 ), ( -88 + 2 = -86 ), ( -86 + 8 = -78 ), ( -78 + 3 = -75 ).
Answer: -75

9. ( 17 – 5 – 3 – 5 )

Solution:
Evaluate left to right:
( 17 – 5 = 12 ), ( 12 – 3 = 9 ), ( 9 – 5 = 4 ).
Answer: 4

10. ( 4 + 3 \times 3 + 1 + 13 + 7 + 7 \times (3 – 4) )

Solution:

  1. Parentheses: ( 3 – 4 = -1 ).
  2. Multiplication: ( 3 \times 3 = 9 ), ( 7 \times -1 = -7 ).
  3. Combine terms:
    [ 4 + 9 + 1 + 13 + 7 – 7 = 27 ].
    Answer: 27

Explanation (300 Words):

Each expression is solved using PEMDAS/BODMAS to ensure accuracy. Parentheses are resolved first to simplify groups of operations. Next, multiplication and division are handled from left to right. Finally, addition and subtraction are performed in sequence from left to right. This structured approach ensures that all steps are followed logically and nothing is skipped, especially when handling both positive and negative numbers or multiple operations in one expression. Calculations must strictly respect this hierarchy to avoid errors.

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