Solve the Nested Arithmetic: What's the Result of 12 - (75 - (48 + 39))?

Q: Why can't I just work from left to right like reading?

Mathematics has a specific order that must be followed! Parentheses always come first, and you must work from the innermost to the outermost. This ensures everyone gets the same correct answer.

Q: What does it mean when I get a negative number inside parentheses?

Negative numbers are completely normal! In this problem, $ 75 - 87 = -12 $. Just remember that subtracting a negative number is the same as adding its positive version.

Q: How do I handle double negatives like 12 - (-12)?

When you subtract a negative number, it becomes addition! Think of it as: $ 12 - (-12) = 12 + 12 = 24 $. The two negative signs cancel out.

Q: Are there any shortcuts for problems like this?

No reliable shortcuts! The step-by-step method prevents errors. Trying to skip steps or do multiple operations at once usually leads to mistakes with nested parentheses.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve the problem together.

00:10 First, always solve the inside of parentheses. Even if there are more parentheses inside.

00:17 Remember, when you multiply a negative number by a positive number, the result is always negative.

00:34 And when you multiply two negative numbers, the result is always positive.

00:51 We'll use the commutative law to rearrange for easier solving. Commutative means the order doesn't change the result.

01:06 Now, solve the equation from left to right, one step at a time.

01:22 And that's how you find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$12-(75-(48+39))=\text{?}$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Evaluate the innermost parentheses
Step 2: Substitute the result and evaluate the next operation
Step 3: Perform the outer subtraction

Let's perform these calculations:

Step 1: Calculate the innermost expression: $48 + 39$ . $48 + 39 = 87$ .

Step 2: Substitute back into the larger expression: $75 - 87$ . This results in $75 - 87 = -12$ .

Step 3: Substitute this result into the outer expression: $12 - (-12)$ . Since subtracting a negative is equivalent to addition: $12 + 12 = 24$ .

Therefore, the solution to the problem is $24$ .

3

Final Answer

24

Key Points to Remember

Essential concepts to master this topic

Rule: Always work from innermost parentheses to outermost parentheses
Technique: Substitute each result: 48 + 39 = 87, then 75 - 87 = -12
Check: Verify by working backwards: 12 - (-12) = 12 + 12 = 24 ✓

Common Mistakes

Avoid these frequent errors

Ignoring the order of operations and working left to right
Don't solve 12 - 75 first = -63! This skips the nested parentheses and gives completely wrong answers. Always solve innermost parentheses first, then 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 can't I just work from left to right like reading?

+

Mathematics has a specific order that must be followed! Parentheses always come first, and you must work from the innermost to the outermost. This ensures everyone gets the same correct answer.

What does it mean when I get a negative number inside parentheses?

+

Negative numbers are completely normal! In this problem, $75 - 87 = -12$ . Just remember that subtracting a negative number is the same as adding its positive version.

How do I handle double negatives like 12 - (-12)?

+

When you subtract a negative number, it becomes addition! Think of it as: $12 - (-12) = 12 + 12 = 24$ . The two negative signs cancel out.

What if I make a calculation error in the middle steps?

+

That's why checking is so important! If your final answer doesn't make sense, go back and verify each step. Double-check your arithmetic: 48 + 39, then 75 - 87, then 12 - (-12).

Are there any shortcuts for problems like this?

+

No reliable shortcuts! The step-by-step method prevents errors. Trying to skip steps or do multiple operations at once usually leads to mistakes with nested parentheses.

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Solve the Nested Arithmetic: What's the Result of 12 - (75 - (48 + 39))?

Order of Operations with Nested Parentheses

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