Solve the Expression: 4+0.4-0 Step by Step

Q: Why doesn't adding or subtracting zero change the number?

Zero is called the additive identity because it's neutral in addition and subtraction. Think of it like this: if you have 4 apples and add 0 more, you still have 4 apples!

Q: Is this the same for all numbers?

Yes! The identity properties work for any number: $ 10 + 0 = 10 $, $ -5 + 0 = -5 $, and $ 2.7 - 0 = 2.7 $.

Q: What about multiplication and division with zero?

That's different! Multiplying by zero gives zero ($ 4 \times 0 = 0 $), but multiplying by 1 keeps the number unchanged ($ 4 \times 1 = 4 $).

Q: How do I remember these identity properties?

Think of zero as 'doing nothing' in addition and subtraction. It's like adding or removing nothing from what you already have - your amount stays the same!

Q: Why do both expressions equal the same thing?

Both $ 4 + 0 $ and $ 4 - 0 $ equal 4 because zero doesn't change the original number in either operation. That's why we use the equals sign (=) to compare them.

Identity Properties with Zero Operations

$4+0?4-0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Match the correct sign

00:06 Any number plus 0 always equals the number itself

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

00:21 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

$4+0?4-0$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Apply the addition identity property.
Step 2: Apply the subtraction identity property.
Step 3: Compare the results of both expressions.

Now, let's work through each step:

Step 1: For $4 + 0$ , using the addition identity property, we know $4 + 0 = 4$ .

Step 2: For $4 - 0$ , using the subtraction identity property, we find $4 - 0 = 4$ .

Step 3: Comparing the results, we have $4 = 4$ .

Therefore, the solution to the problem is $=$ , which corresponds to the answer choice id="3".

Final Answer

Key Points to Remember

Essential concepts to master this topic

Addition Identity: Adding zero to any number equals the original number
Subtraction Identity: Subtracting zero from 4 gives 4
Verification: Compare both results: 4 + 0 = 4 and 4 - 0 = 4 ✓

Common Mistakes

Avoid these frequent errors

Treating zero operations as changing the value
Don't think that 4 + 0 = 5 or 4 - 0 = 3! Zero is the additive identity, meaning it doesn't change any number when added or subtracted. Always remember that any number plus zero equals itself, and any number minus zero equals itself.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why doesn't adding or subtracting zero change the number?

Zero is called the additive identity because it's neutral in addition and subtraction. Think of it like this: if you have 4 apples and add 0 more, you still have 4 apples!

Is this the same for all numbers?

Yes! The identity properties work for any number: $10 + 0 = 10$ , $-5 + 0 = -5$ , and $2.7 - 0 = 2.7$ .

What about multiplication and division with zero?

That's different! Multiplying by zero gives zero ( $4 \times 0 = 0$ ), but multiplying by 1 keeps the number unchanged ( $4 \times 1 = 4$ ).

How do I remember these identity properties?

Think of zero as 'doing nothing' in addition and subtraction. It's like adding or removing nothing from what you already have - your amount stays the same!

Why do both expressions equal the same thing?

Both $4 + 0$ and $4 - 0$ equal 4 because zero doesn't change the original number in either operation. That's why we use the equals sign (=) to compare them.

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