Solve 9-((-9)+(-4)): Order of Operations with Negative Numbers

Order of Operations with Parentheses

9−((−9)+(−4))= 9-((-9)+(-4))=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:05 Note, positive times negative will always be negative
00:12 Always solve parentheses first
00:22 Note, negative times negative will always be positive
00:28 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

9−((−9)+(−4))= 9-((-9)+(-4))=

2

Step-by-step solution

According to the order of operations, we first address the second parentheses:

Remember that a product of addition and subtraction results in a negative outcome, therefore:

+(−4)=−4 +(-4)=-4

The exercise obtained is:

9−(−9−4)= 9-(-9-4)=

Now we solve the exercise within parentheses:

(−9−4)=−13 (-9-4)=-13

The exercise obtained is:

9−(−13)= 9-(-13)=

Remember that a product of addition and addition results in a positive outcome, therefore:

−(−13)=+13 -(-13)=+13

9+13=22 9+13=22

3

Final Answer

22 22

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always solve operations inside parentheses first
  • Technique: Simplify (-9) + (-4) = -13 before outer operation
  • Check: Substitute back: 9 - (-13) = 9 + 13 = 22 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring parentheses and working left to right
    Don't solve 9 - (-9) = 18 first and then subtract 4 = wrong answer 14! This skips the parentheses rule and changes the problem completely. Always solve what's inside parentheses before doing operations outside.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I solve the parentheses first instead of going left to right?

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The order of operations (PEMDAS/BODMAS) requires parentheses first! This ensures everyone gets the same answer. Without this rule, 9−((−9)+(−4)) 9-((-9)+(-4)) could have multiple different answers.

How do I add two negative numbers like (-9) + (-4)?

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When adding two negatives, add their absolute values and keep the negative sign. So (-9) + (-4) = -(9 + 4) = -13.

What does the double negative 9 - (-13) mean?

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Subtracting a negative is the same as adding the positive! So 9 - (-13) becomes 9 + 13 = 22. Remember: two negatives make a positive.

Can I remove the parentheses right away?

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Only if you're careful with signs! 9−((−9)+(−4)) 9-((-9)+(-4)) becomes 9−(−9)−(−4) 9-(-9)-(-4) , which is 9+9+4 9+9+4 . But it's safer to solve inside parentheses first.

What if I get confused with all the negative signs?

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Break it down step by step! First solve (−9)+(−4)=−13 (-9)+(-4)=-13 . Then you have 9−(−13) 9-(-13) . Finally, 9+13=22 9+13=22 . Take your time with each step.

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