Solve (7×4)÷0: Understanding Division by Zero

Q: Why can't we just say the answer is 0?

Because division asks "what number times 0 gives us 28?" Since any number times 0 equals 0 (not 28), there's no possible answer. That's why we say it's undefined or meaningless.

Q: What if I have 0 ÷ 0 instead?

$ 0 \div 0 $ is also undefined! While any number times 0 equals 0, we can't determine which specific number is the answer, so it remains indeterminate.

Q: Do I still need to do the multiplication first?

Yes! Always follow order of operations (PEMDAS/BODMAS). Calculate $ 7 \times 4 = 28 $ first, then recognize that $ 28 \div 0 $ is undefined.

Q: Will my calculator show an error for this?

Yes! Most calculators will display "ERROR" or "UNDEFINED" when you try to divide by zero. This confirms that the operation is impossible.

Division by Zero with Order of Operations

$(7\times4):0=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Always solve parentheses first

00:09 According to math rules, division by 0 is not allowed

00:13 Therefore there is no solution

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(7\times4):0=$

Step-by-step solution

To solve this problem, we must evaluate the expression $(7 \times 4) : 0$ .

Step 1: Calculate the product $7 \times 4$ .
$7 \times 4 = 28$ .

Step 2: Evaluate the result $28 : 0$ .
In mathematics, division by zero is undefined. This means that it's impossible to calculate $28 \div 0$ because there is no number that multiplied by zero gives 28. Therefore, the entire expression is meaningless.

Conclusion: Because division by zero is undefined, the expression $(7 \times 4) : 0$ is meaningless. Therefore, the correct answer is: The expression is meaningless.

Final Answer

The expression is meaningless.

Key Points to Remember

Essential concepts to master this topic

Rule: Division by zero is always undefined in mathematics
Technique: Evaluate multiplication first: $7 \times 4 = 28$ , then recognize $28 \div 0$ is undefined
Check: Ask "What number times 0 equals 28?" - no answer exists ✓

Common Mistakes

Avoid these frequent errors

Thinking division by zero equals zero
Don't assume $28 \div 0 = 0$ because it seems logical! This creates mathematical contradictions since 0 × 0 ≠ 28. Always remember that division by zero is undefined and makes the entire expression meaningless.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why can't we just say the answer is 0?

Because division asks "what number times 0 gives us 28?" Since any number times 0 equals 0 (not 28), there's no possible answer. That's why we say it's undefined or meaningless.

What if I have 0 ÷ 0 instead?

$0 \div 0$ is also undefined! While any number times 0 equals 0, we can't determine which specific number is the answer, so it remains indeterminate.

Do I still need to do the multiplication first?

Yes! Always follow order of operations (PEMDAS/BODMAS). Calculate $7 \times 4 = 28$ first, then recognize that $28 \div 0$ is undefined.

Is this the same as having no solution?

Not quite! "No solution" means an equation can't be satisfied. Undefined means the mathematical operation itself doesn't exist or make sense in our number system.

Will my calculator show an error for this?

Yes! Most calculators will display "ERROR" or "UNDEFINED" when you try to divide by zero. This confirms that the operation is impossible.

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