Solve the Nested Arithmetic Expression: 79 - (35 - (-9)) - (10 + 43)

Q: Why does subtracting a negative become addition?

When you subtract a negative number, it's like removing a debt. So $ 35 - (-9) $ means "35 minus negative 9" which becomes 35 plus 9. The two negatives cancel out!

Q: Do I really need to follow the exact order?

Yes! Order of operations (PEMDAS) ensures everyone gets the same answer. Without it, $ 79 - (35 - (-9)) $ could be interpreted many different ways and give wrong results.

Q: What if I get confused by all the parentheses?

Work from the innermost parentheses outward. First solve $ (-9) $, then $ (35 - (-9)) $, then $ (10 + 43) $. Take it one step at a time!

Q: How can I check if -18 is really the right answer?

Substitute back into the original: $ 79 - 44 - 53 $. Calculate step by step: $ 79 - 44 = 35 $, then $ 35 - 53 = -18 $. It matches!

Q: Why is the answer negative?

Because we're subtracting larger numbers from 79. When $ 44 + 53 = 97 $ is bigger than 79, the result $ 79 - 97 = -18 $ must be negative.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's get ready to solve this problem!

00:11 Always start by solving everything inside the parentheses first.

00:16 Remember, a negative number times another negative number, equals a positive number.

00:23 Now, calculate what’s inside the parentheses.

00:37 Use the distributive law. Break down 79 into 70 plus 9.

00:43 Next, split 44 into 40 plus 4 using the distributive law.

00:49 Now, let's collect the terms together.

00:59 Again, use the distributive law. Split 53 into 50 plus 3.

01:05 Collect all the terms one more time.

01:08 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$79-(35-(-9))-(10+43)=\text{?}$

2

Step-by-step solution

To solve this problem, let's simplify the expression $79 - (35 - (-9)) - (10 + 43)$ :

First, evaluate the expression inside the first parentheses:

$35 - (-9)$ is equivalent to $35 + 9$ (since subtracting a negative number is equivalent to adding its positive counterpart).
Thus, we have $35 + 9 = 44$ .

Second, evaluate the expression inside the second parentheses:

$10 + 43 = 53$ .

Now substitute these values back into the original expression:

$79 - 44 - 53$ .

Finally, perform the subtraction sequentially:

Calculate $79 - 44 = 35$ .
Then, calculate $35 - 53 = -18$ .

Therefore, the solution to the expression is $-18$ .

Checking against the given choices, the correct choice is:

Choice 2: $18-$ corresponds to $-18$ .

3

Final Answer

18-

Key Points to Remember

Essential concepts to master this topic

Order: Evaluate parentheses first, then subtract from left to right
Technique: Convert $35 - (-9)$ to $35 + 9 = 44$
Check: Substitute back: $79 - 44 - 53 = -18$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring parentheses and calculating left to right
Don't calculate 79 - 35 = 44 first! This ignores the parentheses and gives a completely wrong result. The parentheses change the order and meaning of operations. Always evaluate expressions inside parentheses before doing any other calculations.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does subtracting a negative become addition?

+

When you subtract a negative number, it's like removing a debt. So $35 - (-9)$ means "35 minus negative 9" which becomes 35 plus 9. The two negatives cancel out!

Do I really need to follow the exact order?

+

Yes! Order of operations (PEMDAS) ensures everyone gets the same answer. Without it, $79 - (35 - (-9))$ could be interpreted many different ways and give wrong results.

What if I get confused by all the parentheses?

+

Work from the innermost parentheses outward. First solve $(-9)$ , then $(35 - (-9))$ , then $(10 + 43)$ . Take it one step at a time!

How can I check if -18 is really the right answer?

+

Substitute back into the original: $79 - 44 - 53$ . Calculate step by step: $79 - 44 = 35$ , then $35 - 53 = -18$ . It matches!

Why is the answer negative?

+

Because we're subtracting larger numbers from 79. When $44 + 53 = 97$ is bigger than 79, the result $79 - 97 = -18$ must be negative.

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Solve the Nested Arithmetic Expression: 79 - (35 - (-9)) - (10 + 43)

Order of Operations with Negative Numbers

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