Solve (-8)+(+12): Adding Integers with Different Signs

Q: Why don't I just add 8 and 12 to get 20?

Because the signs are different! When you have different signs (+ and -), you subtract instead of add. Think of it as taking away 8 from 12.

Q: How do I know which sign the answer should have?

The answer takes the sign of the number with the larger absolute value. Since $ |12| > |8| $, and 12 is positive, the answer is positive: +4.

Q: What if the negative number was bigger?

If you had $ (-12) + (+8) $, you'd still subtract: 12 - 8 = 4, but since $ |-12| > |8| $ and -12 is negative, your answer would be -4.

Q: Is there an easier way to think about this?

Yes! Use the number line method. Start at the first number, then move right for positive and left for negative. Starting at -8 and moving 12 steps right gets you to +4.

Integer Addition with Different Signs

Solve the following equation:

$(-8)+(+12)=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Find point (-8) on the axis

00:10 Move to the right (positive) direction on the axis

00:15 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

Solve the following equation:

$(-8)+(+12)=\text{ ?}$

Step-by-step solution

First, let's remember the rule:

$+(+x)=+x$

Now let's write the exercise in the following way:

$-8+12=$

We'll draw a number line and place minus 8 on it, then move 12 steps to the right:

Therefore:

$-8+12=4$

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding integers with different signs means subtract and keep the larger sign
Technique: $-8+12$ becomes subtract 8 from 12 to get 4
Check: Use number line: start at -8, move 12 steps right, land at 4 ✓

Common Mistakes

Avoid these frequent errors

Adding the absolute values instead of subtracting
Don't add 8 + 12 = 20! This ignores the different signs and gives the wrong answer. When signs are different, you must subtract the smaller absolute value from the larger one. Always subtract: 12 - 8 = 4, then take the sign of the larger number.

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 don't I just add 8 and 12 to get 20?

Because the signs are different! When you have different signs (+ and -), you subtract instead of add. Think of it as taking away 8 from 12.

How do I know which sign the answer should have?

The answer takes the sign of the number with the larger absolute value. Since $|12| > |8|$ , and 12 is positive, the answer is positive: +4.

What if the negative number was bigger?

If you had $(-12) + (+8)$ , you'd still subtract: 12 - 8 = 4, but since $|-12| > |8|$ and -12 is negative, your answer would be -4.

Is there an easier way to think about this?

Yes! Use the number line method. Start at the first number, then move right for positive and left for negative. Starting at -8 and moving 12 steps right gets you to +4.

What does the parentheses around the numbers mean?

The parentheses help separate the numbers from their signs. $(-8) + (+12)$ makes it clear that -8 is negative and +12 is positive, preventing confusion with the operation signs.

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