Solve (-3) + (-3): Adding Negative Numbers on a Number Line

Q: Why does adding negative numbers give a more negative result?

Think of negative numbers as debts. If you have a debt of $3 and add another debt of $3, you now owe $6 total! Adding negatives always moves you further from zero on the number line.

Q: How do I know which direction to move on the number line?

Easy rule: Positive numbers move right, negative numbers move left. Since we're adding $ -3 $, we move 3 steps to the left from our starting point.

Q: What's the difference between (-3) + (-3) and 3 - 3?

Completely different! $ (-3) + (-3) = -6 $ because you're adding two negative values. But $ 3 - 3 = 0 $ because you're subtracting a positive from a positive.

Q: Can I just ignore the signs and add 3 + 3?

Never ignore the signs! The negative signs are crucial. $ (-3) + (-3) = -6 $, not $ 6 $. Signs tell you the direction on the number line.

Q: How can I remember this rule?

Think: "Same signs, add and keep the sign". Both numbers are negative, so add their values (3 + 3 = 6) and keep the negative sign to get -6.

Addition of Negative Numbers with Number Lines

$(-3)+(-3)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 The number is oriented and negative

00:09 The negative direction on the axis is to the left, so we'll go 3 to the left

00:17 The number is oriented and negative:

00:20 The negative direction on the axis is to the left, so we'll go 3 to the left

00:32 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

$(-3)+(-3)=$

Step-by-step solution

Let's locate negative 3 on the number line.

Since negative 3 is less than 0, we'll move three steps left 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 $+(-3)$

and negative 3 is less than 0, we'll move three steps left from negative 3, where each step represents one whole number as follows:

We can see that we arrived at negative 6.

Final Answer

$-6$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding negative numbers moves left on the number line
Technique: Start at -3, move 3 steps left: -4, -5, -6
Check: Count total distance from zero: 6 steps left = -6 ✓

Common Mistakes

Avoid these frequent errors

Confusing addition with subtraction when seeing negative signs
Don't think (-3) + (-3) means subtract = 0! The plus sign means ADD negative 3, not subtract it. Always remember: adding negative numbers makes the result MORE negative, moving further left on the number line.

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 negative numbers give a more negative result?

Think of negative numbers as debts. If you have a debt of $3 and add another debt of$ 3, you now owe $6 total! Adding negatives always moves you further from zero on the number line.

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

Easy rule: Positive numbers move right, negative numbers move left. Since we're adding $-3$ , we move 3 steps to the left from our starting point.

What's the difference between (-3) + (-3) and 3 - 3?

Completely different! $(-3) + (-3) = -6$ because you're adding two negative values. But $3 - 3 = 0$ because you're subtracting a positive from a positive.

Can I just ignore the signs and add 3 + 3?

Never ignore the signs! The negative signs are crucial. $(-3) + (-3) = -6$ , not $6$ . Signs tell you the direction on the number line.

How can I remember this rule?

Think: "Same signs, add and keep the sign". Both numbers are negative, so add their values (3 + 3 = 6) and keep the negative sign to get -6.

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