Solve: 13-(10-((-4)-(-10))) Using Order of Operations

Nested Parentheses with Negative Numbers

13(10((4)(10)))= 13-(10-((-4)-(-10)))=

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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 brackets first, the rule also applies within brackets
00:08 Note, minus multiplied by minus becomes positive
00:20 Calculate the most "inner" brackets first
00:29 Now calculate the outer brackets
00:36 And now we can solve the exercise
00:39 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

13(10((4)(10)))= 13-(10-((-4)-(-10)))=

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.

13(10((4)(10)))= 13-(10-((-4)-(-10))) =

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.

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.

13(10((4)(10)))=13(10((4)+10)) 13-(10-((-4)-(-10))) = 13-(10-((-4)+10))

Reminder: addition and subtraction of directed numbers

When we have two numbers with different signs, it is important to determine which number is greater in terms of absolute value (absolute - the distance from zero). The larger number will determine the sign of the result and we will perform a subtraction exercise.

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

13(4)=134=9 13-(4) = 13-4 = 9

Therefore, the correct answer is c: (9)

3

Final Answer

9 9

Key Points to Remember

Essential concepts to master this topic
  • Rule: Work from innermost to outermost parentheses first
  • Technique: (-4)-(-10) becomes (-4)+10 = 6
  • Check: Substitute final result back through each step: 13-4 = 9 ✓

Common Mistakes

Avoid these frequent errors
  • Working parentheses from left to right instead of innermost first
    Don't solve 13-(10-...) before handling the innermost (-4)-(-10) = wrong order of operations! This creates calculation errors and wrong final answers. Always start with the deepest nested 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?

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The order of operations (PEMDAS/BODMAS) requires you to handle parentheses from the inside out. Think of nested parentheses like layers of an onion - you peel away the innermost layer first!

What happens when I subtract a negative number?

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Subtracting a negative is the same as adding the positive! So (4)(10) (-4) - (-10) becomes (4)+10=6 (-4) + 10 = 6 . Remember: two negatives make a positive.

How do I keep track of all these parentheses?

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Work step by step and rewrite the expression after each calculation. Use different colors or underline the part you're working on. Don't try to do multiple steps in your head!

What if I get confused with the negative signs?

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Take your time with sign rules:

  • Same signs: positive result
  • Different signs: negative result
When in doubt, use a number line to visualize the operations.

Can I work from left to right instead?

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No! You must follow the order of operations. Parentheses always come before other operations, and nested parentheses must be solved from innermost to outermost.

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