Evaluate the Expression: 0 ÷ (10-3) Using Order of Operations

Zero Division with Parentheses Operations

0:(103)= 0:(10-3)=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

0:(103)= 0:(10-3)=

2

Step-by-step solution

To solve this problem, we need to follow these steps:

  • Step 1: Simplify inside the parentheses 10310 - 3.
  • Step 2: Calculate the division 0:(103)0 : (10 - 3) using the result from Step 1.

Let's go through these steps:
Step 1: Simplify the expression inside the parentheses.
Calculate 103=710 - 3 = 7.
Step 2: Evaluate the division step 0:70 : 7.
Any number divided by zero is undefined, but zero divided by any non-zero number is 00.
Therefore, 0:7=00 : 7 = 0.

Hence, the solution to the problem is 00.

Among the choices provided, the correct answer is:

  • Choice 4: 00
3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Always solve parentheses first, then division operations
  • Technique: Calculate 103=7 10 - 3 = 7 , then 0÷7=0 0 ÷ 7 = 0
  • Check: Zero divided by any non-zero number always equals zero ✓

Common Mistakes

Avoid these frequent errors
  • Dividing 10 and 3 by zero separately
    Don't calculate 0 ÷ 10 and 0 ÷ 3 separately = wrong approach! The parentheses mean you must subtract first. Always solve parentheses completely before dividing: (10 - 3) = 7, then 0 ÷ 7 = 0.

Practice Quiz

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\( 1\times1000= \)

FAQ

Everything you need to know about this question

Why can't I divide the zero by each number in the parentheses?

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The parentheses create a single group that must be calculated first! You can't split 0÷(103) 0 ÷ (10-3) into separate divisions because that changes the mathematical meaning completely.

What's the difference between 0 ÷ 7 and 7 ÷ 0?

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Huge difference! 0÷7=0 0 ÷ 7 = 0 (zero divided by any number is zero), but 7÷0 7 ÷ 0 is undefined (you can't divide by zero).

Do I always get zero when zero is in the numerator?

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Yes! When zero is divided by any non-zero number, the result is always zero. Think of it as: how many groups of 7 can you make from 0 items? Zero groups!

What if I forgot about order of operations?

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You'd get the wrong answer! Always remember PEMDAS/BODMAS: Parentheses (or Brackets) come first, then division. Write out each step to avoid mistakes.

Is there a quick way to recognize this pattern?

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Yes! Whenever you see 0 divided by anything (except zero itself), the answer is immediately 0. But still show your work by solving the parentheses first!

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