Solve the Arithmetic Expression: 124 - (38 - 92) - (56 + 33)

Order of Operations with Negative Numbers

124(3892)(56+33)=? 124-(38-92)-(56+33)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Negative times positive always equals negative
00:08 Negative times negative always equals positive
00:14 Negative times positive always equals negative
00:22 Use the distribution law and split 124 into 120 plus 4
00:28 Use the distribution law and split 38 into 30 and 8
00:32 Use the distribution law and split 92 into 90 plus 2
00:35 Use the distribution law and split 56 into 50 and 6
00:44 Use the distribution law and split 33 into 30 and 3
00:47 Let's group the tens
01:05 Let's solve one operation at a time
01:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

124(3892)(56+33)=? 124-(38-92)-(56+33)=\text{?}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Evaluate the expression inside the first parentheses, (3892) (38-92) .
  • Step 2: Evaluate the expression inside the second parentheses, (56+33) (56+33) .
  • Step 3: Substitute these results back into the main expression and simplify.

Now, let's work through each step:

Step 1: Calculate 3892 38 - 92 .
This results in 54-54.

Step 2: Calculate 56+33 56 + 33 .
This equals 8989.

Step 3: Substitute these values into the original expression:
124(54)89 124 - (-54) - 89 .

  • First, simplify 124(54) 124 - (-54) .
    Subtracting a negative is equivalent to adding its positive, so this becomes:
    124+54=178 124 + 54 = 178 .
  • Next, subtract 89:
    17889=89 178 - 89 = 89 .

Therefore, the solution to the problem is 89 89 .

3

Final Answer

89

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always solve parentheses first, then work left to right
  • Technique: Subtracting negatives becomes addition: 124 - (-54) = 124 + 54
  • Check: Verify each step: (38-92)=-54, (56+33)=89, final answer=89 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring negative signs when simplifying
    Don't change 124 - (-54) to 124 - 54 = 70! This ignores the double negative rule and gives wrong answers. Always remember that subtracting a negative number means adding its positive value.

Practice Quiz

Test your knowledge with interactive questions

\( 70:(14\times5)= \)

FAQ

Everything you need to know about this question

Why does subtracting a negative become addition?

+

Think of it as removing a debt! If you owe -$54, removing that debt gives you +$54. So 124(54)=124+54 124 - (-54) = 124 + 54 .

What if I get confused with all the parentheses?

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Work step by step! First solve what's inside each set of parentheses separately. Write down: (38-92) = -54 and (56+33) = 89. Then substitute these values back.

How do I remember the order of operations?

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Use PEMDAS: Parentheses first, then Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). For this problem, we only need the P and AS parts!

Can I solve this a different way?

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You could expand everything first, but it's much easier to follow order of operations. Parentheses help organize your work and prevent mistakes with negative numbers.

What if my calculator gives a different answer?

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Make sure you enter parentheses correctly! Many calculators need you to type: 124 - ( 38 - 92 ) - ( 56 + 33 ) exactly as written.

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