Solve Division Expression: 106÷(6+1-5) Step by Step

Order of Operations with Parentheses Division

Solve the following expression:

106:(6+15)= 106:(6+1-5)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this math expression together.
00:11 First up, always tackle what's inside the parentheses.
00:16 Split 106 into 100 plus 6, using the distribution law.
00:22 Be sure to divide each part inside the parentheses by the factor outside.
00:28 Solve each division separately, then add them up.
00:33 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following expression:

106:(6+15)= 106:(6+1-5)=

2

Step-by-step solution

Let's simplify this expression while maintaining the order of operations.

Let's start by solving the expression in parentheses from left to right:

6+15=75=2 6+1-5=7-5=2

Now we get the expression:

106:2= 106:2=

In the next step, to make the division easier for ourselves, we'll break down 106 into two smaller factors that are divisible by 2:

(100+6):2= (100+6):2=

Let's divide each factor in parentheses by 5:

(100:2)+(6:2)= (100:2)+(6:2)=

We'll solve each expression in parentheses and obtain:

50+3=53 50+3=53

3

Final Answer

53 53

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always solve parentheses first before any other operations
  • Technique: Break down division: 106÷2=(100÷2)+(6÷2)=50+3 106÷2 = (100÷2) + (6÷2) = 50+3
  • Check: Verify parentheses calculation: 6+15=2 6+1-5 = 2 , then 106÷2=53 106÷2 = 53

Common Mistakes

Avoid these frequent errors
  • Solving division before parentheses
    Don't calculate 106÷6 first = 17.67! This ignores the order of operations and gives completely wrong results. Always solve what's inside parentheses first, then perform division.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

\( (85+5):10= \)

FAQ

Everything you need to know about this question

Why can't I just divide 106 by 6 first?

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Because of the order of operations (PEMDAS)! The parentheses must be solved first. If you divide by 6 first, you're ignoring the +1-5 part completely, which changes the entire problem.

Do I have to break down 106 into 100+6?

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No, that's just one helpful method! You can also directly calculate 106÷2=53 106÷2 = 53 . Breaking it down makes division easier, especially with larger numbers.

What if the parentheses had multiplication or division?

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Same rule applies! Always solve everything inside parentheses first, following PEMDAS within the parentheses too (multiplication/division before addition/subtraction).

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 when checking?

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Go back and check your parentheses calculation first! Make sure 6+15=2 6+1-5 = 2 . Then verify 106÷2=53 106÷2 = 53 . Most errors happen in the parentheses step.

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