Solve the Addition Problem: -30 + 30 Step by Step

Q: Why does -30 + 30 equal 0 and not 60?

Because you're adding opposite numbers (additive inverses)! The negative 30 and positive 30 cancel each other out completely, leaving zero.

Q: How do I remember which direction to move on the number line?

Positive numbers: move right. Negative numbers: move left. So +30 means move 30 steps to the right from wherever you start.

Q: What if the numbers were different, like -20 + 30?

Start at -20, then move 30 steps right. You'll land at +10 because you moved further right than your starting negative position.

Q: Is there a faster way than using the number line?

Yes! When you see a number and its exact opposite being added (like -30 + 30), you can instantly say the answer is 0 without drawing anything.

Integer Addition with Additive Inverses

$-30+30=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 The number is directed, and negative

00:09 The negative direction on the axis is left, so we'll take 30 to the left

00:25 The number is directed, and positive

00:31 The positive direction on the axis is right, so we'll take 30 to the right

00:39 And we returned to point 0

00:45 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

$-30+30=$

Step-by-step solution

Let's locate negative 30 on the number line.

Since negative 30 is less than 0, we'll move thirty steps to the left of zero, where each step represents one whole number as follows:

Now let's look at the operation in the exercise, since the operation is $+30$

And since 30 is greater than 0, we'll move thirty steps to the right from negative 30, where each step represents one whole number as follows:

We can see that the number we reached is 0.

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Additive Inverse Rule: Any number plus its opposite always equals zero
Number Line Method: Start at -30, move 30 steps right to reach 0
Verification: Check that -30 + 30 = 0 using additive inverse property ✓

Common Mistakes

Avoid these frequent errors

Adding absolute values instead of using signed addition
Don't add |-30| + |30| = 30 + 30 = 60! This ignores the negative sign completely and gives the wrong answer. Always keep track of positive and negative signs when adding integers.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why does -30 + 30 equal 0 and not 60?

Because you're adding opposite numbers (additive inverses)! The negative 30 and positive 30 cancel each other out completely, leaving zero.

How do I remember which direction to move on the number line?

Positive numbers: move right. Negative numbers: move left. So +30 means move 30 steps to the right from wherever you start.

What if the numbers were different, like -20 + 30?

Start at -20, then move 30 steps right. You'll land at +10 because you moved further right than your starting negative position.

Is there a faster way than using the number line?

Yes! When you see a number and its exact opposite being added (like -30 + 30), you can instantly say the answer is 0 without drawing anything.

What's the difference between -30 + 30 and 30 - 30?

Both equal 0! Subtracting 30 from 30 gives the same result as adding -30 to 30. They're just different ways to write the same mathematical idea.

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