Solve the Expression: 2+3×6-3×7+1 Using Order of Operations

Order of Operations with Mixed Integer Terms

Complete the exercise:

2+3×63×7+1= 2+3\times6-3\times7+1=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Remember! Multiply and divide before you add and subtract.
00:22 Add and subtract from left to right, as they're the same in the order.
00:31 Let's rearrange using the commutative property for simplicity.
00:35 Now, solve it step-by-step from left to right again.
00:42 And that's your solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the exercise:

2+3×63×7+1= 2+3\times6-3\times7+1=

2

Step-by-step solution

According to the rules of the order of arithmetic operations, we must first solve the multiplication exercises.

We place them inside of parentheses in order to avoid confusion during the solution:

2+(3×6)(3×7)+1= 2+(3\times6)-(3\times7)+1=

We then solve the multiplication exercises:

2+1821+1= 2+18-21+1=

Lastly we solve the rest of the exercise from left to right:

2+18=20 2+18=20

2021=1 20-21=-1

1+1=0 -1+1=0

3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Multiplication comes before addition and subtraction operations
  • Technique: Calculate 3×6=18 3\times6=18 and 3×7=21 3\times7=21 first
  • Check: Substitute back: 2+1821+1=0 2+18-21+1=0

Common Mistakes

Avoid these frequent errors
  • Solving left to right without following order of operations
    Don't calculate 2+3=5 first, then 5×6=30! This ignores multiplication priority and gives wrong answers like 7 or 17. Always multiply 3×6 and 3×7 before adding or subtracting.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why can't I just solve from left to right?

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Mathematics has a specific order of operations (PEMDAS) that everyone follows. If we solved left to right, the same expression could have different answers depending on who solves it!

What does PEMDAS stand for again?

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Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Remember: Please Excuse My Dear Aunt Sally!

Should I use parentheses like in the solution?

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Adding parentheses around multiplication like (3×6) (3\times6) is helpful for clarity but not required. It helps you see which operations to do first!

What if I get a negative number in the middle?

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That's normal! In this problem, we get 2021=1 20-21=-1 . Just continue with the remaining operations: 1+1=0 -1+1=0 .

How can the answer be zero?

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Zero is a valid answer! It means all the positive and negative terms perfectly cancel out. Always double-check by substituting back into the original expression.

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