Solve -58-((-7)-(-12)): Order of Operations with Negative Numbers

Parentheses Operations with Double Negatives

58((7)(12))= -58-((-7)-(-12))=

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Step-by-step video solution

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00:00 Solve
00:03 Note - negative times negative is always positive
00:11 Always solve parentheses first
00:20 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

58((7)(12))= -58-((-7)-(-12))=

2

Step-by-step solution

According to the order of operations, we first solve the exercise within parentheses:

Remember that the product of a negative by a negative results in a positive, therefore:

(12)=+12 -(-12)=+12

We obtain the exercise:

58(7+12)= -58-(-7+12)=

We solve the exercise within parentheses:

7+12=5 -7+12=5

Now we obtain:

585=63 -58-5=-63

3

Final Answer

63 -63

Key Points to Remember

Essential concepts to master this topic
  • Order: Always solve innermost parentheses first, then work outward
  • Technique: Change -(-12) to +12 before calculating (-7)+12 = 5
  • Check: Verify final calculation: -58-5 = -63 matches the correct answer ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the double negative rule
    Don't leave -(-12) as -12 = gives -58-(-19) = -39 instead of -63! The double negative must become positive. Always change -(-number) to +number before solving parentheses.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why does -(-12) become +12?

+

The double negative rule says that subtracting a negative is the same as adding a positive. Think of it as: minus a minus equals plus. So (12)=+12 -(-12) = +12 .

Do I solve both sets of parentheses at the same time?

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No! Work from the inside out. First handle the double negative (12)=+12 -(-12) = +12 , then solve (7)+12=5 (-7) + 12 = 5 , finally calculate 585 -58 - 5 .

What if I accidentally treat -(-12) as just -12?

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You'll get the wrong answer! If you use -12 instead of +12, you get (7)+(12)=19 (-7) + (-12) = -19 , then 58(19)=39 -58 - (-19) = -39 instead of the correct -63.

How can I remember the double negative rule?

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Think of it like "two wrongs make a right" or use the phrase "minus times minus equals plus." The two negative signs cancel each other out!

Should I use PEMDAS for this problem?

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Yes! The P in PEMDAS means Parentheses first. Always solve what's inside parentheses before doing any other operations like subtraction or addition.

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