Solve: 73-(89-(37-45)) Using Order of Operations

Order of Operations with Nested Parentheses

Solve the following problem:

73(89(3745))= 73-(89-(37-45))=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's solve this problem together.
00:12 First, focus on solving the expressions inside the parentheses.
00:17 Remember, always start with the innermost parentheses.
00:23 A negative times a negative equals a positive. Keep that in mind!
00:28 Now, let's solve the outer parentheses with what we have.
00:35 And that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

73(89(3745))= 73-(89-(37-45))=

2

Step-by-step solution

Adhering to the order of operations: First calculate any operations inside of the parentheses. Next proceed to the multiplication and division operations (left to right) and finally address the addition and subtraction operations.(left to right)

When there are parentheses within parentheses, we start with the innermost ones first.

73(89(3745))= 73-(89-(37-45))=


In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation in the inner parentheses, after which we can remove the inner parentheses and be left with only one set of parentheses.

73(89(3745))=73(89(8)) 73-(89-(37-45))=73-(89-(-8))

Pay attention

When an exercise contains a sequence of two signs (which are usually separated by parentheses) we distinguish between several cases:

When there is a sequence of two plus signs, the result will be plus.

When there is a sequence of two minus signs, the result will be plus.

When there is a sequence of minus and plus or plus and minus, the result will be minus.

73(89(8))=73(89+8) 73-(89-(-8)) = 73-(89+8)
Now we'll perform the operation in the remaining parentheses and after calculating we'll eventually remove the parentheses

73(89+8)=73(97) 73-(89+8)= 73-(97)


73(97)=7397 73-(97) = 73-97

Reminder - Adding and Subtracting Signed Numbers

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

7397=24 73-97 = -24

Therefore the answer is option c - (-24)

3

Final Answer

24 -24

Key Points to Remember

Essential concepts to master this topic
  • Rule: Work from innermost to outermost parentheses first
  • Technique: 3745=8 37-45 = -8 , then 89(8)=89+8 89-(-8) = 89+8
  • Check: Verify each step: 7397=24 73-97 = -24

Common Mistakes

Avoid these frequent errors
  • Working left to right without following parentheses order
    Don't calculate 73-89 first = wrong starting point! This ignores the nested parentheses and breaks the order of operations. Always start with the innermost parentheses and work your way 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 (37-45) instead of the first numbers I see?

+

The order of operations requires you to handle parentheses first, and when parentheses are nested, you must start with the innermost ones. Think of it like peeling an onion - work from the inside out!

What happens when I subtract a negative number like 89-(-8)?

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Subtracting a negative is the same as adding a positive! So 89(8)=89+8=97 89-(-8) = 89+8 = 97 . Remember: two negatives make a positive.

How do I keep track of all these parentheses without getting confused?

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Write out each step clearly and only remove one set of parentheses at a time. Start with the innermost calculation, then rewrite the entire expression with that result before moving to the next level.

Why is my answer negative when I'm subtracting smaller numbers?

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In 7397 73-97 , you're subtracting a larger number from a smaller number, which always gives a negative result. The absolute difference is 24, but since 97 > 73, the answer is -24.

Can I use a calculator for problems like this?

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Yes, but be very careful with parentheses! Make sure you enter them exactly as written. It's often better to work step-by-step by hand first to understand the process.

What if I get a different negative number as my answer?

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Double-check your sign rules! The most common errors are in handling 89(8) 89-(-8) (should become 89+8) and the final subtraction 7397 73-97 (should be negative).

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