Solve the Nested Expression: Breaking Down 304 - (94 + (45 - (9 - 35)))

Q: Why do I start with (9 - 35) instead of 304 - 94?

The order of operations (PEMDAS) requires you to solve parentheses first, starting with the innermost ones. Think of nested parentheses like Russian dolls - you must open the smallest one first!

Q: What does 45 - (-26) actually mean?

When you subtract a negative number, it becomes addition! $ 45 - (-26) = 45 + 26 = 71 $. Remember: two negatives make a positive.

Q: How can I avoid getting confused with all these parentheses?

Try color-coding or numbering each set of parentheses. Work from the inside out, writing down each step. For example: Step 1: (9-35) = -26, Step 2: (45-(-26)) = 71, etc.

Q: What if I get a different answer when I redo the problem?

Don't panic! Go through each step slowly and compare with your first attempt. Look for sign errors (like forgetting that subtracting a negative becomes positive) or calculation mistakes.

Q: Are there any shortcuts for nested parentheses?

Not really - you must follow the proper order! But you can organize your work by rewriting the expression after each step: $ 304-(94+(45-(-26))) $, then $ 304-(94+71) $, etc.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Always solve parentheses first, even within parentheses

00:10 Note, negative times positive always equals negative

00:15 Note, negative times negative always equals positive

00:34 Note, negative times positive always equals negative

00:46 Note, negative times negative always equals positive

01:01 Solve from left to right, one operation at a time

01:22 Break down 71 into 70 and 1, so it will be easier to solve

01:29 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

$304-(94+(45-(9-35)))=\text{?}$

2

Step-by-step solution

To solve the expression $304-(94+(45-(9-35)))$ , we will follow these steps:

Step 1: Begin with the innermost parentheses: $(9-35)$ .
Calculation: $9 - 35 = -26$ .
Step 2: Substitute this result into the next part: $(45 - (-26))$ .
Calculation: $45 + 26 = 71$ (Recall that subtracting a negative number is equivalent to adding its absolute value).
Step 3: Substitute this result back into the expression: $94 + 71$ .
Calculation: $94 + 71 = 165$ .
Step 4: Substitute this result into the outermost expression: $304 - 165$ .
Calculation: $304 - 165 = 139$ .

Therefore, the solution to the problem $304-(94+(45-(9-35)))$ is $139$ .

3

Final Answer

139

Key Points to Remember

Essential concepts to master this topic

Rule: Work from innermost parentheses outward systematically
Technique: Subtracting negative numbers: $45 - (-26) = 45 + 26 = 71$
Check: Verify each step: $304 - 165 = 139$ matches final answer ✓

Common Mistakes

Avoid these frequent errors

Working from left to right instead of innermost parentheses first
Don't solve 304 - 94 = 210 first and then work with remaining terms = wrong answer 36! This ignores the nested parentheses structure and gives incorrect results. Always start with the deepest nested parentheses and work outward step by step.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why do I start with (9 - 35) instead of 304 - 94?

+

The order of operations (PEMDAS) requires you to solve parentheses first, starting with the innermost ones. Think of nested parentheses like Russian dolls - you must open the smallest one first!

What does 45 - (-26) actually mean?

+

When you subtract a negative number, it becomes addition! $45 - (-26) = 45 + 26 = 71$ . Remember: two negatives make a positive.

How can I avoid getting confused with all these parentheses?

+

Try color-coding or numbering each set of parentheses. Work from the inside out, writing down each step. For example: Step 1: (9-35) = -26, Step 2: (45-(-26)) = 71, etc.

Is there a way to check my work?

+

Yes! You can substitute your final answer back, or work backwards. Also, estimate: 304 is close to 300, and we're subtracting about 165, so 139 seems reasonable (not too big or small).

What if I get a different answer when I redo the problem?

+

Don't panic! Go through each step slowly and compare with your first attempt. Look for sign errors (like forgetting that subtracting a negative becomes positive) or calculation mistakes.

Are there any shortcuts for nested parentheses?

+

Not really - you must follow the proper order! But you can organize your work by rewriting the expression after each step: $304-(94+(45-(-26)))$ , then $304-(94+71)$ , etc.

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Solve the Nested Expression: Breaking Down 304 - (94 + (45 - (9 - 35)))

Order of Operations with Nested Parentheses

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