Finding the Sum: Adding Negative Numbers a + b

Addition Rules with Two Negative Numbers

a is negative number.

b is negative number.

What is the sum of a+b?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

a is negative number.

b is negative number.

What is the sum of a+b?

2

Step-by-step solution

 

Let's check an example:

Let's say a = -1

b = -2

 

-1 + (-2) =

-1-2= 

-3

 

As the example shows us, what we can also do with additional examples,

is that adding two negative numbers will always result 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: Add absolute values, then make result negative: |-3| + |-5| = 8, so -3 + (-5) = -8
  • Check: Use number line: start at first negative, move left by second negative amount ✓

Common Mistakes

Avoid these frequent errors
  • Thinking negative plus negative might give positive
    Don't assume that adding negatives could give a positive result = completely wrong answer! This happens when students confuse addition with subtraction or multiplication rules. Always remember: negative + negative = more negative.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-\frac{1}{2})= \)

FAQ

Everything you need to know about this question

Why is negative plus negative always negative?

+

Think of negative numbers as debts. If you owe $3 and then owe another $5, your total debt is $8 (negative). Adding debts makes your debt bigger, not smaller!

How is this different from multiplying negatives?

+

Great question! Multiplication of two negatives gives positive (like -2 × -3 = 6), but addition of negatives stays negative. Don't mix up these rules!

Can I use a number line to visualize this?

+

Absolutely! Start at the first negative number, then move left (more negative direction) by the amount of the second negative number. You'll always land further left (more negative).

What if the numbers are very close to zero?

+

Even tiny negative numbers follow the same rule! 0.1+(0.2)=0.3 -0.1 + (-0.2) = -0.3 . The sum is still negative, just closer to zero than larger negative numbers.

Is there ever an exception to this rule?

+

Never! This is a fundamental rule of mathematics. As long as both numbers are truly negative (less than zero), their sum will always be negative. No exceptions!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations