Solve Division Expression: 12÷(4×2-9÷3) Step-by-Step Solution

Order of Operations with Mixed Division

12:(4×293)= 12:(4\times2-\frac{9}{3})=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this math problem together!
00:08 First, we tackle what’s inside the parentheses.
00:12 Next, focus on multiplication and division.
00:17 Divide nine by three. You've got this!
00:21 After solving the parentheses, move forward.
00:29 And there you have it! We've found the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12:(4×293)= 12:(4\times2-\frac{9}{3})=

2

Step-by-step solution

Given that, according to the rules of the order of operations, parentheses come first, we will first solve the exercise that appears within the parentheses.

4×293= 4\times2-\frac{9}{3}=

We solve the multiplication exercise:

4×2=8 4\times2=8

We divide the fraction (numerator by denominator)93=3 \frac{9}{3}=3

And now the exercise obtained within the parentheses is83=5 8-3=5

Finally, we divide:12:5=125 12:5=\frac{12}{5}

3

Final Answer

125 \frac{12}{5}

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always solve parentheses first, then multiplication and division
  • Technique: In parentheses: 4×2=8 4\times2=8 and 93=3 \frac{9}{3}=3 , then 83=5 8-3=5
  • Check: Substitute back: 12:(4×293)=12:5=125 12:(4\times2-\frac{9}{3}) = 12:5 = \frac{12}{5}

Common Mistakes

Avoid these frequent errors
  • Solving from left to right without following PEMDAS
    Don't solve 12÷4 first = 3, then 3×2-9÷3 = wrong answer! This ignores the parentheses rule and gives incorrect results. Always solve everything inside parentheses completely before moving to operations outside.

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 solve from left to right?

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The order of operations (PEMDAS) is a mathematical rule that ensures everyone gets the same answer! Parentheses always come first, so you must solve 4×293 4\times2-\frac{9}{3} completely before dividing by 12.

Do I solve multiplication or division first inside the parentheses?

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Inside parentheses, you still follow PEMDAS! So solve multiplication and division from left to right: 4×2=8 4\times2=8 and 93=3 \frac{9}{3}=3 , then subtract: 83=5 8-3=5 .

Why is my answer a fraction instead of a decimal?

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Both 125 \frac{12}{5} and 2.4 are correct! In math, we often leave answers as improper fractions because they're exact. Decimals like 2.4 are also acceptable.

What if there were no parentheses in this problem?

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Without parentheses, you'd solve: 12÷4×29÷3 12÷4×2-9÷3 from left to right for multiplication/division: 63=3 6-3=3 . The parentheses completely change the order!

How do I check if my final answer is right?

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Substitute your result back into the original expression. Since 4×293=5 4×2-\frac{9}{3}=5 , you should get 12÷5=125 12÷5=\frac{12}{5} . If it matches your answer, you're correct!

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