Solve the Expression: -45-(8+10) Using Order of Operations

Order of Operations with Negative Numbers

45(8+10)= -45-(8+10)=

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Step-by-step video solution

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00:00 Solve
00:03 Always solve parentheses first
00:09 Now we'll continue solving as usual
00:12 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

45(8+10)= -45-(8+10)=

2

Step-by-step solution

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

8+10=18 8+10=18

Now we obtain the exercise:

45(18)= -45-(18)=

We open the parentheses, remember to change the corresponding sign:

4518=63 -45-18=-63

3

Final Answer

63 -63

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Always solve parentheses first, then left to right
  • Technique: Calculate 8+10=18, then evaluate -45-18
  • Check: Verify -45-18 equals -63 by counting backward ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring parentheses and working left to right
    Don't solve -45-8+10 = -43! This ignores PEMDAS order and gives the wrong answer. Always solve what's inside parentheses first: (8+10)=18, then -45-18=-63.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(30-21)= \)

FAQ

Everything you need to know about this question

Why do I have to do the parentheses first?

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The order of operations (PEMDAS) is a universal math rule! Parentheses always come first, no matter what. Think of parentheses as a package - you must unwrap it completely before using what's inside.

How do I subtract a positive number from a negative?

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When you see 4518 -45 - 18 , think of it as moving further left on the number line. Start at -45, then move 18 more spaces left to reach -63.

What if I accidentally got -43 instead?

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You probably calculated -45 - 8 + 10 instead of solving the parentheses first! Remember:

  • Wrong way: -45 - 8 + 10 = -43
  • Right way: -45 - (8 + 10) = -45 - 18 = -63

Is there a trick to remember the order of operations?

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Yes! Remember PEMDAS: Please Excuse My Dear Aunt Sally

  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)

Why is the answer negative?

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We start with -45 (already negative) and then subtract 18 more. Subtracting makes negative numbers even more negative! Think: if you owe $45 and then spend $18 more, you now owe $63.

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