Solve the Expression: 2-6÷2+5×2 Using Order of Operations

Order of Operations with Mixed Division Notation

Complete the exercise:

26:2+5×2= 2-6:2+5\times2=

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Step-by-step video solution

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00:01 Multiplication and division operations precede addition and subtraction
00:13 Addition and subtraction - solve from left to right

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the exercise:

26:2+5×2= 2-6:2+5\times2=

2

Step-by-step solution

According to the rules of the order of arithmetic operations, we must first place the multiplication and division exercises within parentheses:

2(6:2)+(5×2)= 2-(6:2)+(5\times2)=

We then solve the exercise inside of the parentheses:

6:2=3 6:2=3

5×2=10 5\times2=10

We obtain the following exercise:

23+10= 2-3+10=

Finally we solve the exercise from left to right:

23=1 2-3=-1

1+10=9 -1+10=9

3

Final Answer

9

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Multiplication and division happen before addition and subtraction
  • Left to Right: Solve 6÷2=3 6÷2=3 and 5×2=10 5×2=10 first
  • Final Check: 23+10=9 2-3+10=9 matches our answer ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following order of operations
    Don't solve 2-6÷2+5×2 as (2-6)÷2+5×2 = -2! This ignores PEMDAS and gives the wrong result. Always do multiplication and division first, then addition and subtraction from left to right.

Practice Quiz

Test your knowledge with interactive questions

\( 8 + 3 \times 2 = \)

FAQ

Everything you need to know about this question

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

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Order of operations (PEMDAS) is a mathematical rule that everyone follows! Without it, the same expression could have multiple answers, which would make math confusing and unreliable.

What does the colon symbol (:) mean in math?

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The colon (:) means division, just like the ÷ symbol. So 6:2 6:2 is the same as 6÷2=3 6÷2=3 .

Do I need parentheses when solving this?

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You don't need to write parentheses, but adding them like 2(6:2)+(5×2) 2-(6:2)+(5×2) can help you visualize 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, 23=1 2-3=-1 , but then we add 10 to get 1+10=9 -1+10=9 . Keep going until you finish all operations.

How do I remember the order of operations?

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Use the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Some students remember it as "Please Excuse My Dear Aunt Sally"!

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