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]=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

What is the result of the following equation?

\( 36-4\div2 \)

FAQ

Everything you need to know about this question

Why do I solve 6÷3 before 26-6÷3?

+

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?

+

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?

+

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?

+

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?

+

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.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Order of Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations