Solve Division Problem: 225÷[(26-6÷3)×5] Using Order of Operations

Order of Operations with Nested Brackets

225:[(266:3)×5]= 225:[(26-6:3)\times5]=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's tackle this problem together!
00:10 Always start by solving inside the parentheses.
00:14 And remember, solve the innermost parentheses first.
00:18 Multiplication and division come before addition and subtraction.
00:23 Now, let's work on these parentheses step by step.
00:33 Next, solve what’s inside the square brackets before moving on.
00:43 Write the division as a fraction. This makes it easier!
00:47 Break down 225 into 15 times 15.
00:53 And for 120, break it into 15 times 8.
00:57 Simplify everything you can; it helps a lot!
01:02 And there you have it—that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

225:[(266:3)×5]= 225:[(26-6:3)\times5]=

2

Step-by-step solution

First, we solve the exercise within the innermost parentheses:

(266:3)= (26-6:3)=

According to the order of operations, we first divide and then subtract:

262=24 26-2=24

Now we obtain the exercise:

225:(24×5)= 225:(24\times5)=

We solve the multiplication exercise and then divide:

225:120=1.875 225:120=1.875

3

Final Answer

1.875

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then division/multiplication, finally addition/subtraction
  • Technique: Work innermost brackets out: 6÷3=2 6÷3=2 , then 262=24 26-2=24
  • Check: Verify each step: 24×5=120 24×5=120 , then 225÷120=1.875 225÷120=1.875

Common Mistakes

Avoid these frequent errors
  • Working left to right instead of following order of operations
    Don't solve 225÷26 first = 8.65, then subtract 6÷3! This ignores brackets and gives completely wrong results. Always work from innermost brackets outward, following PEMDAS strictly.

Practice Quiz

Test your knowledge with interactive questions

\( 20\div(4+1)-3= \)

FAQ

Everything you need to know about this question

Why do I solve 6÷3 before 26-6÷3?

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Because division comes before subtraction in PEMDAS! Within the brackets (26-6÷3), you must divide first: 6÷3 = 2, then subtract: 26-2 = 24.

What if I accidentally solve 26-6 first?

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You'd get (26-6)÷3 = 20÷3 = 6.67, which is wrong! The brackets don't change the order of operations inside them - division still comes before subtraction.

How do I keep track of all the steps?

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Write each step clearly:

  • Step 1: 225÷[(266÷3)×5] 225÷[(26-6÷3)×5]
  • Step 2: 225÷[(262)×5] 225÷[(26-2)×5]
  • Step 3: 225÷[24×5] 225÷[24×5]
  • Step 4: 225÷120=1.875 225÷120 = 1.875

Can I use a calculator for this?

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Yes, but be careful with parentheses! Enter it exactly as written: 225÷((26-6÷3)×5). Missing parentheses will give the wrong answer.

Why is my answer a decimal instead of a whole number?

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That's normal! 225÷120 225÷120 doesn't divide evenly, so 1.875 is the correct decimal answer. Not all division problems result in whole numbers.

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