Solve: [(124+8):4+16:2]+(12·3-3):11 - Order of Operations Challenge

Order of Operations with Nested Brackets

Solve the following problem:

[(124+8):4+16:2]+(1233):11= [(124+8):4+16:2]+(12\cdot3-3):11=

❤️ 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
00:12 Let's solve this exercise together!
00:15 First, focus on solving the parentheses.
00:20 Remember, inside the parentheses, follow the order of operations.
00:26 Do multiplication and division before addition and subtraction.
00:33 Keep solving step by step, using the correct order of operations.
00:45 And there you have it, the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

[(124+8):4+16:2]+(1233):11= [(124+8):4+16:2]+(12\cdot3-3):11=

2

Step-by-step solution

Simplify the following expression whilst following the order of operations. The order of operations states that exponents precede multiplication and division, which in turn precede addition and subtraction, and that parentheses precede all of the above:

Therefore, begin by simplifying the expressions inside of the parentheses first, noting that in this problem there are two pairs of parentheses. Thus we'll simplify gradually, starting with the expression inside of the left parentheses in the first term on the left and perform the addition within them. Simultaneously begin simplifying the expression in the right parentheses, following the order of operations mentioned above. Hence we'll perform the multiplication operation first:

(124+8):4+16:2+(1233):11=132:4+16:2+(363):11 (124+8):4+16:2+(12\cdot3-3):11= \\ 132:4+16:2+(36-3):11

Continue simplifying the expression, by completing the simplification of the remaining right parentheses. Proceed to the subtraction operation, and simultaneously perform the division operations in the first two terms of the expression that we obtained in the last step. This leaves us with the addition operations between all terms for the end in accordance with the order of operations:

132:4+16:2+(363):11=33+8+33:11 132:4+16:2+(36-3):11 =\\ 33+8+33:11

Let's continue, again performing first the division operation in the third term from the left and finally performing the addition operations:

33+8+33:11=33+8+3=44 33+8+33:11 =\\ 33+8+3=\\ 44

Shown below are the various steps we took to simplify the given expression:

(124+8):4+16:2+(1233):11=33+8+3=44 (124+8):4+16:2+(12\cdot3-3):11= \\ 33+8+3=\\ 44

Therefore, the correct answer is answer D.

3

Final Answer

44

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then division/multiplication left to right
  • Technique: Work inside out: (124+8)=132, then 132÷4=33
  • Check: Final calculation 33+8+3=44 matches answer choice D ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without respecting parentheses
    Don't solve 124+8÷4 first = 126! This ignores parentheses and gives wrong results. Always complete all operations inside parentheses before moving to operations outside them.

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 have to do the parentheses first?

+

Parentheses are like mathematical containers - you must finish everything inside before you can use that result! Think of it like unwrapping a gift box before you can see what's inside.

What's the difference between ÷ and : symbols?

+

They mean exactly the same thing - division! The colon (:) is just another way to write division, commonly used in some countries. So 16:2 = 16÷2 = 8.

How do I handle multiple sets of parentheses?

+

Work on each set separately but at the same time if they're independent. In this problem, solve (124+8)(124+8) and (1233)(12\cdot3-3) separately since they don't affect each other.

Why did we get 33 from the last division?

+

After simplifying the parentheses, we had (363):11=33:11=3(36-3):11 = 33:11 = 3. Remember that 33÷11=3 because 11×3=33!

Can I use a calculator for these problems?

+

While calculators help, it's important to understand the steps first! Practice doing these by hand so you really understand the order of operations - this builds your math foundation.

🌟 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