Solve 5 + (-6) Using Number Line Visualization

Q: 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.

Q: 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!

Q: 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.

Q: 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 $

Q: 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.

Integer Addition with Negative Numbers

$5+(-6)=$

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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

Understand the problem

$5+(-6)=$

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:

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

Since the operation is $+(-6)$

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:

We can see that we reached the number minus 1.

Final Answer

$-1$

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 $5 + (-6) = -1$ 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

Solve the following expression:

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

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: $10 + (-3) = 7$

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.

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