Solve 15?15=0: Finding the Correct Operation Sign

Q: Why does subtracting a number from itself always give zero?

Think of it as taking away exactly what you have. If you have 15 apples and take away 15 apples, you have zero apples left! This works for any number.

Q: Could division also work since 15 ÷ 15 = 1?

No, because we need the result to be zero, not one. Division of identical non-zero numbers always equals 1, never 0.

Q: What if the numbers were different, like 20 ? 5 = 0?

Then no basic operation would work! You can't get zero from two different positive numbers using +, -, ×, or ÷.

Q: Is there a shortcut to solve these problems?

Yes! When you see identical numbers and need zero, subtraction is almost always the answer. But always verify by checking the calculation.

Inverse Operations with Identical Numbers

Choose the correct sign (?):

$15\text{?}15=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's identify which operations are correct.

00:09 If you subtract a number from itself, it equals zero. So, this operation is a match.

00:23 Dividing a number by itself gives you one. This operation does not fit.

00:35 Adding numbers means increasing their value. That's not a match.

00:42 And that's the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct sign (?):

$15\text{?}15=0$

Step-by-step solution

To solve this problem, we need to determine which arithmetic operation between two identical numbers, 15, results in zero.

Step 1: Consider the operation of subtraction. For any number $a$ , the subtraction $a - a$ equals zero.
Step 2: Apply this to the problem. Subtracting 15 from 15 is $15 - 15$ , which equals 0. This satisfies the condition given in the problem.
Step 3: Verify against other operations:
- Addition: $15 + 15 = 30$ , not zero.
- Multiplication: $15 \times 15 = 225$ , not zero.
- Division: $15 \div 15 = 1$ , not zero.

Since subtraction is the only operation resulting in zero, the correct sign is a minus sign.

Therefore, the correct answer is $-$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Subtracting any number from itself always equals zero
Technique: Test each operation: $15 - 15 = 0$ works
Check: Verify other operations don't work: 15 + 15 = 30 ≠ 0 ✓

Common Mistakes

Avoid these frequent errors

Choosing addition because both numbers are positive
Don't assume positive numbers need addition = 15 + 15 = 30! This ignores that we need zero as the result. Always test what operation actually produces the required answer.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does subtracting a number from itself always give zero?

Think of it as taking away exactly what you have. If you have 15 apples and take away 15 apples, you have zero apples left! This works for any number.

Could division also work since 15 ÷ 15 = 1?

No, because we need the result to be zero, not one. Division of identical non-zero numbers always equals 1, never 0.

What if the numbers were different, like 20 ? 5 = 0?

Then no basic operation would work! You can't get zero from two different positive numbers using +, -, ×, or ÷.

Is there a shortcut to solve these problems?

Yes! When you see identical numbers and need zero, subtraction is almost always the answer. But always verify by checking the calculation.

What if one of the options was 'All answers are correct'?

Be careful! Test each operation individually. In this case, only subtraction works, so 'All answers are correct' would be wrong.

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