Addition of Negative Numbers: Determining the Sum of a + b Where a, b < 0

Integer Addition with Negative Values

a and b are negative numbers.

Therefore, a + b is...?

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Step-by-step written solution

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1

Understand the problem

a and b are negative numbers.

Therefore, a + b is...?

2

Step-by-step solution

To answer the question, we need to remember that when there is a sequence of minus and plus or plus and minus, the result will be minus.

In other words, (-)+ is actually -.

Let's demonstrate with an example:

Let's say a is -1

and b is -2

(-1)+(-2)=-3

And the result is negative!

Let's try to switch between the numbers, and say that a is -2

and b is -1

(-2)+(-1)=-3

The result is still negative!

Therefore we can conclude that adding two negative numbers results in a negative number.

3

Final Answer

Negative

Key Points to Remember

Essential concepts to master this topic
  • Rule: Adding two negative numbers always produces a negative result
  • Technique: Remove parentheses and add: (-3) + (-5) = -8
  • Check: Use number line: move left twice, end up negative ✓

Common Mistakes

Avoid these frequent errors
  • Thinking negative plus negative equals positive
    Don't assume (-) + (-) = (+) like multiplication rules = wrong positive answer! This confuses addition with multiplication. Always remember that adding negatives moves further left on the number line, making the result more negative.

Practice Quiz

Test your knowledge with interactive questions

\( (-2)+3= \)

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666

FAQ

Everything you need to know about this question

Why isn't the sum positive when I add two negatives?

+

Think of negative numbers as debts. If you owe $3 and owe another $2, you now owe $5 total - that's more debt, not less!

How is this different from multiplying negatives?

+

Great question! In multiplication, negative × negative = positive. But in addition, you're combining the values, so negative + negative = more negative.

What if the numbers are really big negatives?

+

The rule stays the same! Whether it's (-1) + (-2) = -3 or (-100) + (-200) = -300, adding negatives always gives a negative result.

Can I use a number line to check this?

+

Absolutely! Start at zero, move left for the first negative, then move left again for the second negative. You'll always end up further left (more negative) than where you started.

What happens if one number is much smaller than the other?

+

It doesn't matter! Even (-1) + (-1000) = -1001. When both numbers are negative, the sum is always negative, regardless of their sizes.

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