Solve the Expression: Evaluate 17 - (215 - (314 + 95))

Q: Why do I need to solve the innermost parentheses first?

The order of operations (PEMDAS) requires you to work from inside out! If you don't follow this rule, you'll get completely different answers. Always start with $ 314 + 95 = 409 $ first.

Q: What does subtracting a negative number mean?

Subtracting a negative is the same as adding a positive! So $ 17 - (-194) $ becomes $ 17 + 194 = 211 $. Think of it as "taking away a debt" which gives you more.

Q: How do I keep track of all these nested parentheses?

Work one layer at a time from the inside out! First solve $ 314 + 95 $, then substitute to get $ 17 - (215 - 409) $, and continue step by step.

Q: Can I use a different order and still get the right answer?

No! The order of operations must be followed exactly. If you work left to right or skip steps, you'll get wrong answers like -417 or -211 instead of the correct 211.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Negative times positive is always negative

00:08 Negative times negative is always positive

00:18 Let's use the distributive law and split 215 into 200 and 15

00:27 Let's use the distributive law and split 314 into 300 and 14

00:34 Let's use the commutative law and arrange the exercise for easier solving

00:53 Let's solve one operation at a time

01:15 Let's use the distributive law and split 14 into 10 and 4

01:19 Let's use the distributive law and split 95 into 90 and 5

01:29 Let's solve one operation at a time

01:41 And 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

$17-(215-(314+95))=\text{?}$

2

Step-by-step solution

To solve this problem, we'll simplify the expression $17-(215-(314+95))$ step-by-step:

Step 1: Solve the innermost parentheses. Calculate $314 + 95 = 409$ .
Step 2: Substitute back into the expression. We now have $17-(215-409)$ .
Step 3: Simplify the subtraction inside the parentheses. Compute $215 - 409 = -194$ .
Step 4: Substitute back into the expression. We have $17 - (-194)$ .
Step 5: Simplify the subtraction, remembering that subtracting a negative number is equivalent to adding a positive number. So, $17 - (-194) = 17 + 194$ .
Step 6: Perform the final addition. Calculate $17 + 194 = 211$ .

Therefore, the solution to the problem is $211$ .

3

Final Answer

$211$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always work from innermost parentheses outward first
Technique: Calculate 314 + 95 = 409 before any subtraction
Check: Verify 17 - (-194) = 17 + 194 = 211 ✓

Common Mistakes

Avoid these frequent errors

Working left to right ignoring parentheses
Don't calculate 17 - 215 = -198 first and ignore nested parentheses = wrong final answer! This violates the order of operations and creates cascading errors. Always solve the innermost parentheses (314 + 95) first, then work outward.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I need to solve the innermost parentheses first?

+

The order of operations (PEMDAS) requires you to work from inside out! If you don't follow this rule, you'll get completely different answers. Always start with $314 + 95 = 409$ first.

What does subtracting a negative number mean?

+

Subtracting a negative is the same as adding a positive! So $17 - (-194)$ becomes $17 + 194 = 211$ . Think of it as "taking away a debt" which gives you more.

How do I keep track of all these nested parentheses?

+

Work one layer at a time from the inside out! First solve $314 + 95$ , then substitute to get $17 - (215 - 409)$ , and continue step by step.

Can I use a different order and still get the right answer?

+

No! The order of operations must be followed exactly. If you work left to right or skip steps, you'll get wrong answers like -417 or -211 instead of the correct 211.

What's the easiest way to check my work?

+

Use a calculator to verify each step:

Step 1: 314 + 95 = 409
Step 2: 215 - 409 = -194
Step 3: 17 - (-194) = 211

If any step doesn't match, go back and fix it!

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Solve the Expression: Evaluate 17 - (215 - (314 + 95))

Order of Operations with Nested Parentheses

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