Find the Missing Operator in 99?99 = 0: Mathematical Symbol Problem

Q: Why can't addition give us zero?

When you add two positive numbers, you always get a larger positive number. $ 99 + 99 = 198 $, which is much bigger than zero!

Q: What about multiplication - could that work?

Multiplying two positive numbers always gives a positive result. $ 99 \times 99 = 9801 $, which is far from zero. Only multiplying by zero gives zero!

Q: Could division ever equal zero?

Division of equal non-zero numbers always equals 1. $ 99 ÷ 99 = 1 $. For division to equal zero, the numerator must be zero while the denominator is non-zero.

Q: Is subtraction the only way to get zero?

For basic operations with the same number twice, yes! $ a - a = 0 $ for any number a. This is called the subtraction identity property.

Q: How do I remember this rule?

Think of it as "taking away what you have" - if you have 99 items and remove all 99, you're left with 0 items. This makes subtraction the logical choice!

Basic Operations with Zero Results

Choose the correct sign (?):

$99?99=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine which operation(s) are correct

00:03 Select the correct operation

00:07 We will use long addition for calculation

00:12 Adding means increasing the number, so it's definitely not suitable

00:23 We will use long multiplication for calculation

00:58 Multiplying the number means increasing it, so it's not suitable

01:21 We will use long subtraction for calculation

01:34 Any number minus itself always equals 0, suitable

01:42 Any number divided by itself always equals 1, not suitable

01:57 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct sign (?):

$99?99=0$

Step-by-step solution

To solve this problem, let's test each of the given operators with the number 99 to verify which one results in 0:

$99 + 99$ : This equals $198$ , not $0$ .
$99 \times 99$ : This equals $9801$ , not $0$ .
$99 - 99$ : This operation results in $0$ , which matches our expectation.
$99 : 99$ : Assuming ':' represents division, $99 : 99$ equals $1$ , not $0$ .

Therefore, the operation that satisfies the equation $99 ? 99 = 0$ is subtraction.

Hence, the correct choice is: $-$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Identity Rule: Any number minus itself always equals zero
Technique: Test each operator: 99 - 99 = 0 works
Check: Verify other operators don't work: 99 + 99 = 198 ≠ 0 ✓

Common Mistakes

Avoid these frequent errors

Assuming addition or multiplication could work
Don't think 99 + 99 or 99 × 99 could equal 0 because they give positive results! Adding or multiplying positive numbers never produces zero. Always remember that subtracting a number from itself is the only basic operation that yields zero.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why can't addition give us zero?

When you add two positive numbers, you always get a larger positive number. $99 + 99 = 198$ , which is much bigger than zero!

What about multiplication - could that work?

Multiplying two positive numbers always gives a positive result. $99 \times 99 = 9801$ , which is far from zero. Only multiplying by zero gives zero!

Could division ever equal zero?

Division of equal non-zero numbers always equals 1. $99 ÷ 99 = 1$ . For division to equal zero, the numerator must be zero while the denominator is non-zero.

Is subtraction the only way to get zero?

For basic operations with the same number twice, yes! $a - a = 0$ for any number a. This is called the subtraction identity property.

How do I remember this rule?

Think of it as "taking away what you have" - if you have 99 items and remove all 99, you're left with 0 items. This makes subtraction the logical choice!

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