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

Order of Operations with Nested Parentheses

17−(3⋅5−4⋅2+2⋅3)= 17-(3\cdot5-4\cdot2+2\cdot3)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:04 Always solve the parentheses first
00:07 Multiplication and division precede addition and subtraction
00:16 Solve one multiplication at a time
00:33 Continue to solve the expression according to the correct order of operations
00:46 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

17−(3⋅5−4⋅2+2⋅3)= 17-(3\cdot5-4\cdot2+2\cdot3)=

2

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, let's start by simplifying the expression inside the parentheses, remembering that multiplication comes before addition and subtraction and thus we will first perform the multiplications in this expression, then perform the subtraction operations, and finally complete the calculation by performing the subtraction operation on the expression in parentheses:

17−(3⋅5−4⋅2+2⋅3)=17−(15−8+6)=17−13=4 17-(3\cdot5-4\cdot2+2\cdot3)= \\ 17-(15-8+6)= \\ 17-13= \\ 4

Therefore the correct answer is answer C

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication before addition/subtraction
  • Technique: Calculate 3⋅5−4⋅2+2⋅3=15−8+6=133\cdot5-4\cdot2+2\cdot3 = 15-8+6 = 13
  • Check: Final answer: 17−13=417-13 = 4 matches option C ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following order of operations
    Don't calculate 17-3×5 = 14×5 first = completely wrong path! This ignores that parentheses must be solved first, and multiplication comes before subtraction. Always solve the expression inside parentheses completely before subtracting from 17.

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?

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Mathematical order matters! The order of operations (PEMDAS) ensures everyone gets the same correct answer. Working left to right would give different results and break mathematical consistency.

Do I have to do all multiplications before any additions in the parentheses?

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Yes! Within the parentheses (3⋅5−4⋅2+2⋅3)(3\cdot5-4\cdot2+2\cdot3), you must complete all three multiplications first: 15, 8, and 6, then work left to right with subtraction and addition.

What if I get a different answer like 23 or -4?

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These are common wrong answers! 23 comes from adding instead of subtracting the parentheses result. -4 comes from calculation errors inside the parentheses. Double-check your arithmetic step by step.

How do I remember PEMDAS?

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Use the memory trick "Please Excuse My Dear Aunt Sally" for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Or remember: grouping symbols first, then operations by strength!

Can I use a calculator for this?

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While calculators help with arithmetic, make sure yours follows order of operations correctly! Some basic calculators work left to right. Practice by hand to truly understand the concept.

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