Order of Operations: Evaluating Expression with Division and Multiplication

Order of Operations with Nested Parentheses

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 expression
00:03 Always solve the parentheses first
00:07 Multiplication and division precede addition and subtraction
00:20 Continue to solve the expression according to the proper order of operations
00:23 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

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 these,

Therefore, we'll start by simplifying the expression in parentheses, and since division comes before addition, we'll first perform the division operation in this expression and then the addition operation:

4+(6+6:3)2=4+(6+2)2=4+82 4+(6+6:3)\cdot2= \\ 4+(6+2)\cdot2= \\ 4+8\cdot2 \\ We'll continue to simplify the expression we got in the last step, remembering that multiplication comes before addition and therefore we'll first perform the multiplication in the expression and then the addition operation:

4+82=4+16=20 4+8\cdot2= \\ 4+16= \\ 20 Therefore, the correct answer is answer C.

3

Final Answer

20 20

Key Points to Remember

Essential concepts to master this topic
  • Rule: Parentheses first, then division and multiplication before addition
  • Technique: Work inside out: 6÷3=2, then 6+2=8, then 8×2=16
  • Check: Follow PEMDAS step by step: 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 ignore parentheses = wrong answer 26⅔! This violates PEMDAS rules and gives incorrect results. Always solve 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?

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Order of operations (PEMDAS) ensures everyone gets the same answer! Without these rules, 4+6×2 4+6×2 could equal 20 or 16 - math would be confusing and inconsistent.

What does the colon (:) mean in this problem?

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The colon (:) is another way to write division, just like ÷. So 6:3 6:3 means 6 divided by 3, which equals 2.

Do I solve everything inside parentheses at once?

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No! Even inside parentheses, you still follow order of operations. So in (6+6:3) (6+6:3) , do the division first: 6:3=2 6:3=2 , then addition: 6+2=8 6+2=8 .

How do I remember the order of operations?

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

What if I get a different answer?

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Double-check each step! The most common mistake is ignoring parentheses or doing addition before multiplication. Write out each step clearly and follow PEMDAS exactly.

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