Solve the Equation: Finding the Missing Operation in 4?0=4

Q: Why can both + and - work in the same equation?

Both operations work because of identity properties! Adding zero doesn't change a number, and subtracting zero also doesn't change it. So $ 4 + 0 = 4 $ and $ 4 - 0 = 4 $ are both true.

Q: What about multiplication and division by zero?

Multiplication: Any number times zero equals zero, so $ 4 \times 0 = 0 $, not 4. Division: Division by zero is undefined in mathematics, so we can't use it here.

Q: How do I know when multiple answers are possible?

Always test each operation systematically. Write out: $ 4 + 0 $, $ 4 - 0 $, $ 4 \times 0 $, and $ 4 ÷ 0 $. See which ones equal 4!

Q: Is this type of problem common in math?

Yes! Understanding identity properties is fundamental. These problems help you recognize when zero acts as an identity element (doesn't change the result) versus when it changes everything.

Q: What if the number wasn't 4?

The same rules apply! For any number n, both $ n + 0 = n $ and $ n - 0 = n $ will always be true, while $ n \times 0 = 0 $ (unless n = 0).

Identity Properties with Zero Operations

Choose the correct sign (?):

$4?0=4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the correct mathematical sign

00:03 Any number plus 0 always equals the number itself

00:15 Any number minus 0 always equals the number itself

00:28 Any number multiplied by 0 always equals 0

00:37 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct sign (?):

$4?0=4$

Step-by-step solution

Let's solve this problem by evaluating each operation:

Test Addition: $4 + 0 = 4$ . This operation holds true since adding zero to a number does not change the value of the number.
Test Subtraction: $4 - 0 = 4$ . This operation is also consistent with the rule that subtracting zero from a number keeps the number unchanged.
Test Multiplication: $4 \times 0 = 0$ . This does not satisfy the equation $4 ? 0 = 4$ , as multiplying by zero results in zero rather than four.

From this analysis, the operations "+" and "-" both satisfy the original problem statement $4 ? 0 = 4$ . Therefore, the correct answer must reflect both options.

Therefore, the correct answer is Answers (a) and (b).

Final Answer

Answers (a) and (b)

Key Points to Remember

Essential concepts to master this topic

Identity Rules: Adding or subtracting zero keeps numbers unchanged
Testing Method: Try each operation: $4 + 0 = 4$ and $4 - 0 = 4$
Verification: Both addition and subtraction with zero preserve the original value ✓

Common Mistakes

Avoid these frequent errors

Only testing one operation and stopping
Don't just test addition and assume it's the only answer = missing correct solutions! This leads to incomplete answers when multiple operations work. Always test all four basic operations systematically.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why can both + and - work in the same equation?

Both operations work because of identity properties! Adding zero doesn't change a number, and subtracting zero also doesn't change it. So $4 + 0 = 4$ and $4 - 0 = 4$ are both true.

What about multiplication and division by zero?

Multiplication: Any number times zero equals zero, so $4 \times 0 = 0$ , not 4. Division: Division by zero is undefined in mathematics, so we can't use it here.

How do I know when multiple answers are possible?

Always test each operation systematically. Write out: $4 + 0$ , $4 - 0$ , $4 \times 0$ , and $4 ÷ 0$ . See which ones equal 4!

Is this type of problem common in math?

Yes! Understanding identity properties is fundamental. These problems help you recognize when zero acts as an identity element (doesn't change the result) versus when it changes everything.

What if the number wasn't 4?

The same rules apply! For any number n, both $n + 0 = n$ and $n - 0 = n$ will always be true, while $n \times 0 = 0$ (unless n = 0).

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