Solve -33-(17-3): Order of Operations with Negative Numbers

Parentheses with Negative Number Subtraction

33(173)= -33-(17-3)=

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Step-by-step video solution

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00:00 Solve
00:03 Always solve parentheses first
00:08 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

33(173)= -33-(17-3)=

2

Step-by-step solution

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

173=14 17-3=14

Now we obtain the exercise:

3314=47 -33-14=-47

3

Final Answer

47 -47

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Always solve parentheses first, then work left to right
  • Technique: Calculate 173=14 17-3=14 , then solve 3314 -33-14
  • Check: Substitute back: 33(173)=3314=47 -33-(17-3) = -33-14 = -47

Common Mistakes

Avoid these frequent errors
  • Ignoring parentheses and working left to right
    Don't solve -33-17+3 = -47! This ignores the parentheses rule and changes the problem completely. The parentheses mean you must subtract the entire result of (17-3), not add 3 back. Always solve parentheses first: (17-3) = 14, then -33-14 = -47.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just go left to right: -33-17+3?

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The parentheses change everything! (173) (17-3) must be calculated as one unit first. Going left to right ignores this rule and gives you -47 instead of the correct -47 - wait, that's wrong reasoning!

What does the minus sign before parentheses mean?

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The minus sign means you're subtracting the entire result of what's in parentheses. So 33(173) -33-(17-3) means subtract 14 from -33.

How do I handle negative numbers in subtraction?

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Remember: subtracting a positive number makes the result more negative. 3314 -33-14 means move 14 more units left on the number line from -33.

Can I rewrite this without parentheses?

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Yes! 33(173) -33-(17-3) can become 3317+3 -33-17+3 by distributing the negative sign, but it's easier to solve the parentheses first.

What if I got -19 as my answer?

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You likely calculated 33+173 -33+17-3 instead! This happens when you forget that subtracting parentheses means subtracting the whole result, not changing signs randomly.

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