Solving (-13)+(-12): Adding Negative Numbers on a Number Line

Q: Why do I move left when I see a plus sign?

The plus sign means 'add', but you're adding a negative number. Adding negative numbers always moves you left on the number line, just like adding positive numbers moves you right.

Q: How do I know how many steps to move?

Look at the absolute value of the second number. For +(-12), you move 12 steps to the left. The number tells you the distance, the negative sign tells you the direction.

Q: What's the difference between (-13) + (-12) and (-13) - 12?

There's no difference! Both expressions mean the same thing and both give you -25. Adding a negative number is the same as subtracting a positive number.

Q: Can I just add the numbers and make it negative?

Yes! When adding two negative numbers, you can add their absolute values and make the result negative. So $ |-13| + |-12| = 13 + 12 = 25 $, then make it negative: -25.

Q: What if I lose track of my counting on the number line?

Start over and count carefully, or use the shortcut method: add the numbers without their negative signs (13 + 12 = 25), then make the final answer negative (-25).

Adding Negative Numbers with Visual Movement

Solve the following expression using the number line below:

$(-13)+(-12)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 According to the exercise, we'll start from point 13 on the negative side (left)

00:07 The number is directed and negative

00:11 The negative direction on the axis is to the left, so we'll go 12 units left

00:23 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

Solve the following expression using the number line below:

$(-13)+(-12)=$

Step-by-step solution

Let's first locate negative 13 on the number line.

Now let's deal with the operation in the exercise, given that the operation is $+(-12)$

Since negative 12 is less than 0, we will move twelve steps to the left from negative 13, where each step represents one whole number as follows:

We can see that the number we reached is negative 25.

Final Answer

$-25$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding negative numbers means moving left on number line
Technique: Start at -13, move 12 steps left to reach -25
Check: Count positions: -13 to -25 is exactly 12 steps left ✓

Common Mistakes

Avoid these frequent errors

Moving right when adding negative numbers
Don't move right when you see +(-12) = wrong direction and positive result! The plus sign means 'add' but the negative number still moves you left. Always move left when adding any negative number, regardless of the plus sign.

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 do I move left when I see a plus sign?

The plus sign means 'add', but you're adding a negative number. Adding negative numbers always moves you left on the number line, just like adding positive numbers moves you right.

How do I know how many steps to move?

Look at the absolute value of the second number. For +(-12), you move 12 steps to the left. The number tells you the distance, the negative sign tells you the direction.

What's the difference between (-13) + (-12) and (-13) - 12?

There's no difference! Both expressions mean the same thing and both give you -25. Adding a negative number is the same as subtracting a positive number.

Can I just add the numbers and make it negative?

Yes! When adding two negative numbers, you can add their absolute values and make the result negative. So $|-13| + |-12| = 13 + 12 = 25$ , then make it negative: -25.

What if I lose track of my counting on the number line?

Start over and count carefully, or use the shortcut method: add the numbers without their negative signs (13 + 12 = 25), then make the final answer negative (-25).

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