Solve -38-(24-(17-5)): Multiple Nested Parentheses Problem

Order of Operations with Multiple Nested Parentheses

Solve the following problem:

38(24(175))= -38-(24-(17-5))=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solution
00:03 We always solve parentheses first, the rule applies even within parentheses
00:07 We calculate the most "inner" parentheses first
00:14 Now we calculate the outer parentheses
00:23 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

Solve the following problem:

38(24(175))= -38-(24-(17-5))=

2

Step-by-step solution

Adhering to the order of operations: Begin by calculating what's inside of the parentheses, then proceed to multiplication and division (from left to right), finish with addition and subtraction (from left to right)

When there are parentheses within parentheses, we start with the innermost ones first.

38(24(175))= -38-(24-(17-5)) =

In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation in the inner parentheses, after which we can remove the inner parentheses. We'll continue doing this until there are no more parentheses in the exercise.

38(24(175))=38(24(12)) -38-(24-(17-5)) = -38-(24-(12))

38(24(12))=38(2412) -38-(24-(12)) = -38-(24-12)

Now we'll perform the operation in the remaining parentheses. We'll then proceed to remove the parentheses


38(2412)=38(12) -38-(24-12) = -38-(12)

38(12)=3812 -38-(12) = -38-12

Reminder - Addition and subtraction of numbers with the same sign

When we have two numbers with the same sign (plus or minus), that sign will remain in the result, which will actually be the result of an addition exercise.

3812=50 -38-12 = -50

Therefore the answer is option c - (-50)

3

Final Answer

50 -50

Key Points to Remember

Essential concepts to master this topic
  • Rule: Work from innermost parentheses outward, one layer at a time
  • Technique: First solve (17-5)=12, then (24-12)=12, finally -38-12=-50
  • Check: Verify each step: 12→12→-50 matches the correct answer ✓

Common Mistakes

Avoid these frequent errors
  • Working from left to right ignoring parentheses
    Don't solve -38-24 first = -62, then try to work with remaining parentheses! This violates order of operations and gives wrong results. Always start with the innermost parentheses and work outward.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(30-21)= \)

FAQ

Everything you need to know about this question

Why can't I just solve from left to right?

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The order of operations requires parentheses first! Going left to right ignores this rule and gives wrong answers. Always remember PEMDAS - Parentheses come before everything else.

How do I know which parentheses to solve first?

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Start with the innermost parentheses - the ones with no other parentheses inside them. In 38(24(175)) -38-(24-(17-5)) , solve (17-5) first because it's the deepest nested.

What if I get confused with all the parentheses?

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Try color-coding or numbering each layer of parentheses. Work on one layer at a time, and rewrite the expression after each step to see your progress clearly.

Why does removing parentheses sometimes change signs?

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When you have a minus sign before parentheses like (12) -(12) , it becomes 12 -12 . The negative distributes to everything inside the parentheses.

Can I check my work another way?

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Yes! Try working backwards: if your answer is -50, then 50+38=12 -50 + 38 = -12 , and 2412=12 24 - 12 = 12 , and 175=12 17 - 5 = 12 . Everything should match!

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