Solve Complex Fraction: (21:√49+2)/(8-8) Step-by-Step Solution

Q: Why can't I divide by zero?

Division by zero is undefined in mathematics! Think of division as 'how many times does this number go into that number?' - zero can never go into any number, so it's impossible to calculate.

Q: What should I do when I get 0 in the denominator?

When the denominator equals zero, the expression cannot be solved or is 'undefined'. This is the correct mathematical answer - don't try to force a number!

Q: Did I make a mistake if I get division by zero?

Not necessarily! Sometimes the problem is designed to test if you recognize when an expression is undefined. Always follow order of operations carefully and check your work.

Q: What does the colon symbol mean in 21:7?

The colon (:) means division, just like the ÷ symbol. So $ 21:7 $ is the same as $ 21 \div 7 = 3 $.

Order of Operations with Division by Zero

$\frac{21:\sqrt{49}+2}{8-(2+2\times3)}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's solve this math problem together.

00:15 First, find the square root.

00:23 Remember, solve what’s inside the parentheses first.

00:28 Next, handle multiplication and division before addition and subtraction.

00:33 Solve from left to right following the order of operations.

00:42 Uh-oh, we have a division by zero. We can't do that!

00:48 So, there is no solution for this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{21:\sqrt{49}+2}{8-(2+2\times3)}=$

Step-by-step solution

In the numerator we solve the square root exercise:

$\sqrt{49}=7$

In the denominator we solve the exercise within parentheses:

$(2+2\times3)=$

$2+6=8$

The exercise we now have is:

$\frac{21:7+2}{8-8}=$

We solve the exercise in the numerator of fractions from left to right:

$21:7=3$

$3+2=5$

We obtain the exercise:

$\frac{5}{8-8}=\frac{5}{0}$

Since it is impossible for the denominator of the fraction to be 0, it is impossible to solve the exercise.

Final Answer

Cannot be solved

Key Points to Remember

Essential concepts to master this topic

Order: Solve parentheses, then square roots, then division and multiplication left-to-right
Technique: First solve $\sqrt{49} = 7$ and $(2+2\times3) = 8$
Check: Always verify denominator is not zero before attempting division ✓

Common Mistakes

Avoid these frequent errors

Attempting to divide by zero
Don't continue calculating when denominator equals zero = undefined result! Division by zero is mathematically impossible and makes the entire expression undefined. Always check if denominator equals zero before proceeding with division.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why can't I divide by zero?

Division by zero is undefined in mathematics! Think of division as 'how many times does this number go into that number?' - zero can never go into any number, so it's impossible to calculate.

What should I do when I get 0 in the denominator?

When the denominator equals zero, the expression cannot be solved or is 'undefined'. This is the correct mathematical answer - don't try to force a number!

Did I make a mistake if I get division by zero?

Not necessarily! Sometimes the problem is designed to test if you recognize when an expression is undefined. Always follow order of operations carefully and check your work.

How do I solve the numerator 21:7+2?

Follow order of operations: division comes before addition, so $21 \div 7 = 3$ , then $3 + 2 = 5$ . Work left to right for same-level operations!

What does the colon symbol mean in 21:7?

The colon (:) means division, just like the ÷ symbol. So $21:7$ is the same as $21 \div 7 = 3$ .

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Solve Complex Fraction: (21:√49+2)/(8-8) Step-by-Step Solution

Order of Operations with Division by Zero

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I divide by zero?

What should I do when I get 0 in the denominator?

Did I make a mistake if I get division by zero?

How do I solve the numerator 21:7+2?

What does the colon symbol mean in 21:7?

🌟 Unlock Your Math Potential

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