Solve (-8) + (-12): Adding Two Negative Integers

Q: Why is the answer negative when I'm adding?

When you add two negative numbers, you're combining two debts or losses. Adding -8 and -12 means you have 8 units of debt plus 12 more units of debt, giving you 20 total units of debt, which is -20.

Q: How do I remember the rule for adding negative numbers?

Think of it as "negative + negative = more negative". Just like adding 8 apples and 12 apples gives you 20 apples, adding 8 debts and 12 debts gives you 20 debts!

Q: Can I use a number line to solve this?

Absolutely! Start at -8, then move 12 steps to the left (because you're adding a negative number). You'll land on -20, which is your answer.

Q: What if the parentheses weren't there?

The expression would be $ -8 + -12 $, which means exactly the same thing! The parentheses around negative numbers just make it clearer to read.

Q: How is this different from subtraction?

Great question! $ (-8) + (-12) $ gives -20, while $ (-8) - (-12) $ would give +4 because subtracting a negative is like adding a positive.

Integer Addition with Two Negative Numbers

$(-8)+(-12)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Find the point (-8) on the axis

00:06 Positive times negative is always negative, so we subtract

00:09 To subtract, we move in the left (negative) direction on the axis

00:12 Let's calculate

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

$(-8)+(-12)=$

Step-by-step solution

Let's locate -8 on the number line and move 12 steps to the left.

Let's note that our result is a negative number:

Let's remember the rule:

Now let's write the exercise in the appropriate form and solve it:

$-8-12=-20$

Final Answer

$-20$

Key Points to Remember

Essential concepts to master this topic

Rule: When adding two negative numbers, add their absolute values and keep negative sign
Technique: $(-8) + (-12) = -(8 + 12) = -20$
Check: Start at -8 on number line, move 12 steps left to reach -20 ✓

Common Mistakes

Avoid these frequent errors

Subtracting instead of adding the absolute values
Don't think (-8) + (-12) = -(8 - 12) = -(-4) = 4! This confuses addition with subtraction rules and gives positive instead of negative. Always add the absolute values: -(8 + 12) = -20.

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 is the answer negative when I'm adding?

When you add two negative numbers, you're combining two debts or losses. Adding -8 and -12 means you have 8 units of debt plus 12 more units of debt, giving you 20 total units of debt, which is -20.

How do I remember the rule for adding negative numbers?

Think of it as "negative + negative = more negative". Just like adding 8 apples and 12 apples gives you 20 apples, adding 8 debts and 12 debts gives you 20 debts!

Can I use a number line to solve this?

Absolutely! Start at -8, then move 12 steps to the left (because you're adding a negative number). You'll land on -20, which is your answer.

What if the parentheses weren't there?

The expression would be $-8 + -12$ , which means exactly the same thing! The parentheses around negative numbers just make it clearer to read.

How is this different from subtraction?

Great question! $(-8) + (-12)$ gives -20, while $(-8) - (-12)$ would give +4 because subtracting a negative is like adding a positive.

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