Solve 10 + (-12): Integer Addition on a Number Line

Q: Why do I move left when adding a negative number?

On a number line, positive numbers are to the right and negative numbers are to the left. When you add a negative number like (-12), you're moving in the negative direction, which is leftward!

Q: Is 10 + (-12) the same as 10 - 12?

Yes! Adding a negative is identical to subtracting a positive. So $ 10 + (-12) = 10 - 12 = -2 $. This is a key rule that makes integer arithmetic much easier.

Q: How do I know if my final answer should be positive or negative?

Look at which number has the larger absolute value. Since 12 > 10, and 12 is negative in this problem, your answer will be negative. The result takes the sign of the 'stronger' number.

Q: Can I solve this without using the number line?

Absolutely! You can use the rule: $ 10 + (-12) = 10 - 12 = -2 $. The number line just helps you visualize what's happening with the numbers.

Integer Addition with Negative Numbers

Solve the following problem using the number line below:

$10+(-12)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 Our first number is positive.

00:12 A positive number moves us to the right on the number line.

00:16 So, from zero, let's take ten steps to the right.

00:25 Now, let's look at a negative number.

00:29 A negative number moves us to the left on the number line.

00:34 We'll take twelve steps to the left.

00:43 And that's how we solve this! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem using the number line below:

$10+(-12)=$

Step-by-step solution

We will locate the number 10 on the number line, then move 12 steps to the left from it (since minus 12 is less than zero):

We can see that we have reached the number minus 2.

Final Answer

$-2$

Key Points to Remember

Essential concepts to master this topic

Direction Rule: Adding a negative number means moving left on number line
Technique: Start at 10, move 12 steps left to reach -2
Check: Count positions: 10 → 8 → 6 → 4 → 2 → 0 → -2 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting when seeing negative numbers
Don't think 10 + (-12) = 22 by ignoring the negative sign! This treats (-12) as positive 12 and gives a completely wrong result. Always remember that adding a negative number is the same as subtracting that number: 10 + (-12) = 10 - 12 = -2.

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 do I move left when adding a negative number?

On a number line, positive numbers are to the right and negative numbers are to the left. When you add a negative number like (-12), you're moving in the negative direction, which is leftward!

Is 10 + (-12) the same as 10 - 12?

Yes! Adding a negative is identical to subtracting a positive. So $10 + (-12) = 10 - 12 = -2$ . This is a key rule that makes integer arithmetic much easier.

How do I know if my final answer should be positive or negative?

Look at which number has the larger absolute value. Since 12 > 10, and 12 is negative in this problem, your answer will be negative. The result takes the sign of the 'stronger' number.

What if I lose track while counting on the number line?

Break it into smaller steps! From 10, first move to 0 (that's 10 steps), then continue 2 more steps left to reach -2. Or use the rule: 10 - 12 = -2.

Can I solve this without using the number line?

Absolutely! You can use the rule: $10 + (-12) = 10 - 12 = -2$ . The number line just helps you visualize what's happening with the numbers.

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