Solve (-15)+(-5): Adding Negative Numbers on a Number Line

Q: Why do I move left when adding a negative number?

Adding a negative number like $ +(-5) $ means moving in the negative direction on the number line. Think of it as 'adding negativity' which makes your position more negative (further left).

Q: How is this different from subtracting a positive number?

It's exactly the same! $ (-15) + (-5) $ gives the same result as $ (-15) - 5 $. Both operations move you 5 steps left on the number line.

Q: How do I remember which direction to move?

Use this memory trick: Positive = Right, Negative = Left. When adding negative numbers, you're adding 'leftward movement' to your current position.

Q: Can I just ignore the number line and use rules instead?

The number line shows you the rule visually! Once you understand why adding negatives moves left, you can use the rule: adding negative numbers makes the result more negative.

Adding Negative Numbers with Number Line

Solve the following expression using the number line below:

$(-15)+(-5)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Solution.

00:11 Let's begin at the negative 15 point on the left side of the number line.

00:16 This number is negative.

00:18 Since left is the negative direction, we'll move 5 spaces left.

00:29 And that's how we solve the problem!

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:

$(-15)+(-5)=$

Step-by-step solution

Let's first locate the number negative 15 on the number line.

Now let's deal with the operation in the exercise, given that the operation is $+(-5)$

Since negative 5 is less than 0, we will move five steps to the left from negative 15, where each step represents one whole number as follows:

We can see that the number we reached is negative 20.

Final Answer

$-20$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding negative numbers moves left on the number line
Technique: Start at -15, move 5 steps left: -15 → -20
Check: Count positions from -15 to -20 equals 5 steps ✓

Common Mistakes

Avoid these frequent errors

Moving right instead of left when adding negative numbers
Don't move right when adding (-5) = wrong direction and positive result! Adding negative numbers always means moving left (toward more negative values). Always move left when adding any negative number.

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 adding a negative number?

Adding a negative number like $+(-5)$ means moving in the negative direction on the number line. Think of it as 'adding negativity' which makes your position more negative (further left).

How is this different from subtracting a positive number?

It's exactly the same! $(-15) + (-5)$ gives the same result as $(-15) - 5$ . Both operations move you 5 steps left on the number line.

What if I start with a positive number and add a negative?

Same rule applies! Start at your positive number and move left. For example, $3 + (-7) = -4$ means start at 3, move 7 steps left to reach -4.

How do I remember which direction to move?

Use this memory trick: Positive = Right, Negative = Left. When adding negative numbers, you're adding 'leftward movement' to your current position.

Can I just ignore the number line and use rules instead?

The number line shows you the rule visually! Once you understand why adding negatives moves left, you can use the rule: adding negative numbers makes the result more negative.

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