Solve 17-(3×5-4×2+2×3): Order of Operations Challenge

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

Mathematics has a specific order that must be followed! Without PEMDAS, the expression $ 2+3×4 $ could equal 20 or 14. The order ensures everyone gets the same answer.

Q: What do I do first inside the parentheses?

Inside parentheses, follow PEMDAS again! Do all multiplications first (3×5, 4×2, 2×3), then handle the addition and subtraction from left to right.

Q: How do I handle the subtraction of the entire parentheses?

Think of it as $ 17 + (-1) × (result) $. First solve everything inside the parentheses to get one number, then subtract that entire result from 17.

Order of Operations with Nested Parentheses

$17-(3\times5-4\times2+2\times3)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Always solve the parentheses first

00:07 Multiplication and division precede addition and subtraction

00:10 Solve one multiplication at a time

00:18 Continue to solve the expression according to the correct order of operations

00:36 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$17-(3\times5-4\times2+2\times3)=$

Step-by-step solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

therefore we'll start by simplifying the expression in parentheses, since multiplication comes before addition and subtraction, we'll first perform the multiplications in this expression and then the addition and subtraction operations in the expression, in the next step we'll perform the subtraction operation that applies to the expression in parentheses and finish simplifying the expression:

$17-(3\cdot5-4\cdot2+2\cdot3)= \\ 17-(15-8+6)= \\ 17-13=\\ 4$ Therefore the correct answer is answer C.

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication and division, finally addition and subtraction
Technique: Inside parentheses: 3×5=15, 4×2=8, 2×3=6, then 15-8+6=13
Check: Substitute back: 17-13=4 matches our answer ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't calculate 17-3=14 first = wrong sequence! This ignores the parentheses and multiplication priority, leading to incorrect results. Always solve parentheses completely first, doing all multiplications before additions and subtractions inside them.

Practice Quiz

Test your knowledge with interactive questions

Solve the following problem:

$187\times(8-5)=$

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! Without PEMDAS, the expression $2+3×4$ could equal 20 or 14. The order ensures everyone gets the same answer.

What do I do first inside the parentheses?

Inside parentheses, follow PEMDAS again! Do all multiplications first (3×5, 4×2, 2×3), then handle the addition and subtraction from left to right.

How do I handle the subtraction of the entire parentheses?

Think of it as $17 + (-1) × (result)$ . First solve everything inside the parentheses to get one number, then subtract that entire result from 17.

What if I get a different answer when checking?

Go back and check your multiplication inside the parentheses! Make sure you calculated $15-8+6$ correctly by working left to right after the multiplications.

Why is the order of operations so important?

Without a standard order, mathematical expressions would be ambiguous. PEMDAS ensures that $17-(3×5-4×2+2×3)$ always equals 4, no matter who solves it!

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