Solve 10-(12-(4-12)): Order of Operations with Nested Parentheses

Order of Operations with Multiple Nested Parentheses

10−(12−(4−12))= 10-(12-(4-12))=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Always solve parentheses first, the rule also applies within parentheses
00:07 Calculate the innermost parentheses first
00:14 Note, minus multiplied by minus becomes positive
00:25 Now let's calculate the outer parentheses
00:28 Solve the exercise
00:31 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

10−(12−(4−12))= 10-(12-(4-12))=

2

Step-by-step solution

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

10−(12−(4−12))= 10-(12-(4-12))=

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

Therefore, we will first perform the operation of the inner parentheses. After which we will be able to remove the inner parentheses and will be left with only one pair of parentheses.

10−(12−(4−12))=10−(12−(−8)) 10-(12-(4-12))=10-(12-(-8))

Keep in mind

What happens when there is a sequence of two signs present in the exercise (these are usually separated by parentheses) Let's highlight several different cases:

When a sequence with two plus signs appears, the result will also be a plus.

When a sequence with two minus signs appears, the result will also be a plus.

When a sequence with minus and plus signs or plus and minus signs appears, the result will be minus.

10−(12−(−8))=10−(12+8) 10-(12-(-8)) = 10-(12+8)

Now we will perform the operation of the remaining parentheses and after the calculation, we will remove the parentheses.

10−(12+8)=10−(20) 10-(12+8)=10-(20) 10−(20)=10−20=−10 10-\left(20\right)=10-20=-10

Therefore, the correct answer is option a: (-10)

3

Final Answer

−10 -10

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always work from innermost parentheses outward first
  • Technique: Calculate (4-12) = -8, then (12-(-8)) = 20
  • Check: Work step by step: 10-20 = -10 ✓

Common Mistakes

Avoid these frequent errors
  • Working from left to right instead of innermost parentheses first
    Don't solve 10-12 first = -2, then try -(4-12)! This ignores the nested structure and gives wrong results. Always start with the deepest parentheses and work outward.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why do I start with the innermost parentheses first?

+

The order of operations requires you to handle parentheses before anything else. When parentheses are nested (inside each other), you must work from the inside out to maintain the correct mathematical meaning.

What happens when I have two minus signs together?

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Two minus signs become a plus! For example: −(−8)=+8 -(-8) = +8 . Think of it as "the opposite of negative 8 is positive 8".

How do I keep track of all the parentheses?

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Work one layer at a time. First solve (4−12)=−8 (4-12) = -8 , then substitute to get 12−(−8) 12-(-8) , then solve that to get 20, and finally 10−20=−10 10-20 = -10 .

Can I just remove all parentheses at once?

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No! You must respect the nested structure. Each set of parentheses creates a separate calculation that must be completed before moving to the outer level.

Why is my answer negative?

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That's correct! The expression 10−(12−(4−12)) 10-(12-(4-12)) equals -10. Don't assume the answer must be positive - follow the calculations step by step and trust your work.

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