Solve 4+(6+6÷3)×2: Order of Operations Practice

Order of Operations with Parentheses Priority

Solve the following:

4+(6+6:3)2= 4+(6+6:3)\cdot2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:04 Always solve the parentheses first
00:07 Multiplication and division precede addition and subtraction
00:18 Continue to solve the expression according to the correct order of operations
00:33 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following:

4+(6+6:3)2= 4+(6+6:3)\cdot2=

2

Step-by-step solution

Let's simplify this expression while adhering to the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses take priority over all.

In our expression, there is a term in parentheses that needs to be multiplied. We'll start by simplifying this expression, remembering that division comes before addition, so we'll first perform the division operation within the parentheses and then the addition operation in this expression:

4+(6+6:3)2=4+(6+2)2=4+82= 4+(6+6:3)\cdot2= \\ 4+(6+2)\cdot2= \\ 4+8\cdot2=

Let's continue simplifying the expression we that we got in the last step. Since multiplication comes before addition, we'll first calculate the multiplication in the expression and then perform the addition operation:

4+82=4+16=20 4+8\cdot2= \\ 4+16= \\ 20

To summarise:

4+(6+6:3)2=4+82=20 4+(6+6:3)\cdot2= \\ 4+8\cdot2= \\ 20

Therefore the correct answer is answer C.

3

Final Answer

20

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication/division, then addition/subtraction
  • Technique: Inside parentheses: 6+6÷3=6+2=8 6+6÷3 = 6+2 = 8
  • Check: Work step by step: 4+(6+2)×2 = 4+8×2 = 4+16 = 20 ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following order of operations
    Don't calculate 4+6=10 first and then continue left to right = 34! This ignores parentheses and multiplication priority, giving completely wrong results. Always follow PEMDAS: parentheses first, then multiplication/division, then addition/subtraction.

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?

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Mathematics has specific rules called order of operations (PEMDAS) that ensure everyone gets the same answer. Working left to right would give different results and create confusion in math!

What do I do first inside the parentheses (6+6÷3)?

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Even inside parentheses, follow order of operations! Do division first: 6÷3=2, then addition: 6+2=8. So (6+6÷3) becomes (8).

Why is the answer 20 and not 24?

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Getting 24 means you calculated 4+6=10, then 10+6÷3×2. This ignores parentheses priority! The correct path is: 4+(8)×2 = 4+16 = 20.

How can I remember the order of operations?

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Use PEMDAS: Please Excuse My Dear Aunt Sally

  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)

What if there are no parentheses in the problem?

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Without parentheses, start with multiplication and division (working left to right), then do addition and subtraction (left to right). The order of operations still applies!

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