Solve 5 + (-6) Using Number Line Visualization

Integer Addition with Negative Numbers

5+(6)= 5+(-6)= -6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 The number is directed and positive
00:07 The positive direction on the axis is to the right, so we'll take 5 to the right
00:16 The number is directed and negative
00:21 The negative direction on the axis is to the left, so we'll take 6 to the left
00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

5+(6)= 5+(-6)= -6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

2

Step-by-step solution

Let's locate the number 5 on the number line.

Since the number 5 is greater than 0, we'll move five steps to the right from zero, where each step represents one whole number as follows:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

Now let's look at the operation in the exercise.

Since the operation is +(6) +(-6)

And the number minus 6 is less than 0, we'll move six steps to the left from number 5, where each step represents one whole number as follows:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

We can see that we reached the number minus 1.

3

Final Answer

1 -1

Key Points to Remember

Essential concepts to master this topic
  • Number Line Rule: Adding negative numbers means moving left
  • Technique: Start at 5, move 6 steps left: 5 → 4 → 3 → 2 → 1 → 0 → (-1)
  • Check: Verify 5+(6)=1 5 + (-6) = -1 by counting positions on number line ✓

Common Mistakes

Avoid these frequent errors
  • Moving right when adding negative numbers
    Don't move right when you see +(-6) = moving 6 steps right from 5 gets you 11, not -1! The plus sign doesn't change the direction - negative numbers always move left. Always move left when adding any negative number, regardless of the plus sign in front.

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 does adding a negative number make the result smaller?

+

Adding a negative number is like subtracting! When you add (-6), it's the same as subtracting 6. Think of it as taking away or moving backwards on the number line.

How do I remember which direction to move on the number line?

+

Positive numbers = move right, negative numbers = move left. The sign of the number tells you the direction, not the operation sign in front of it!

What's the difference between 5 + (-6) and 5 - 6?

+

There's no difference! Both expressions equal -1. Adding a negative number gives the same result as subtracting that positive number.

Can I get a positive answer when adding a negative number?

+

Yes! If you start with a bigger positive number than the negative number you're adding. For example: 10+(3)=7 10 + (-3) = 7

How do I visualize this without drawing a number line?

+

Think of it as a balance: you have 5 positive units, then you remove 6 units. You end up owing 1 unit, which is -1.

🌟 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