Adding Negative Numbers: Solve (-5) + (-2) Using Number Line

Addition with Negative Number Movement

(5)+(2)= (-5)+(-2)= -6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666-7-7-7

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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 negative
00:07 The negative direction on the axis is to the left, so we'll go 5 units left
00:21 The number is directed and negative
00:26 The negative direction on the axis is to the left, so we'll go 2 units left
00:35 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)+(2)= (-5)+(-2)= -6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666-7-7-7

2

Step-by-step solution

Let's locate negative 5 on the number line.

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

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666-7-7-7

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

Since the operation is +(2) +(-2)

And negative 2 is less than 0, we'll move two steps to the left from negative 5, where each step represents one whole number as follows:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666-7-7-7

We can see that we reached negative 7.

3

Final Answer

7 -7

Key Points to Remember

Essential concepts to master this topic
  • Number Line Rule: Adding a negative means moving left on the number line
  • Technique: Start at -5, move 2 steps left to reach -7
  • Check: Count positions: -5 (start) → -6 → -7 (final answer) ✓

Common Mistakes

Avoid these frequent errors
  • Moving right when adding negative numbers
    Don't move right when you see + (-2) = moving in the wrong direction! The plus sign doesn't cancel the negative - it tells you to ADD the negative number. Always move LEFT when adding negative numbers 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 do I move left when I see a plus sign?

+

The plus sign means 'add', but you're adding a negative number. Think of it as: 'add negative 2' which means move 2 steps in the negative direction (left) on the number line.

Is (-5) + (-2) the same as -5 - 2?

+

Yes! Adding a negative number gives the same result as subtracting a positive number. Both (5)+(2) (-5) + (-2) and 52 -5 - 2 equal -7.

How do I remember which direction to move?

+

Remember: Negative = Left, Positive = Right. When adding negatives, you're moving further into negative territory (leftward on the number line).

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

+

Same rule applies! Start at your positive number and move left the number of steps shown by the negative number. You might end up at zero or even in negative territory.

Can I just ignore the signs and add the numbers?

+

No! The signs are crucial. (5)+(2)=7 (-5) + (-2) = -7 , but 5+2=7 5 + 2 = 7 . Always pay attention to whether numbers are positive or negative.

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