Solve -4 + (-2): Adding Negative Numbers on a Number Line

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

Think of it this way: adding a negative is like taking away or going backwards. On a number line, backwards means left, so $ -4 + (-2) $ means start at -4 and go 2 steps backward (left).

Q: How is this different from subtraction?

Great question! $ -4 + (-2) $ and $ -4 - 2 $ give the same answer (-6) but think of addition as combining two negative values, while subtraction is taking away a positive value.

Q: What if I get confused about which direction to move?

Use this trick: positive numbers move right (→), negative numbers move left (←). So adding (+3) means 3 steps right, adding (-3) means 3 steps left!

Q: How do I remember that negative + negative = more negative?

Think about temperature! If it's -4°F and drops another 2 degrees, you get -6°F (colder). Negative + negative always gives a more negative result.

Q: Can I just ignore the number line and do this in my head?

The number line helps you visualize the concept, but once you understand it, yes! Just remember: $ -4 + (-2) = -(4 + 2) = -6 $. Add the numbers and keep the negative sign.

Adding Negative Numbers with Number Line

Solve the following problem using the number line below:

$-4+(-2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Let's start from point (-4)

00:08 The number is intentional, negative

00:12 Movement towards the negative side of the axis is to the left

00:16 Let's take 2 jumps to the left towards the negative side

00:21 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 problem using the number line below:

$-4+(-2)=$

Step-by-step solution

We'll locate minus 4 on the number line and move two steps to the left (since minus 2 is less than zero):

We can see that we've arrived at the number minus 6.

Final Answer

$-6$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding a negative number means moving left on the number line
Technique: Start at -4, move 2 steps left for (-2) to reach -6
Check: Count the distance: from -4 to -6 is 2 units left ✓

Common Mistakes

Avoid these frequent errors

Moving right when adding negative numbers
Don't move right when adding (-2) = wrong positive result! Adding negatives always makes numbers smaller (more negative). Always move left on the number line when adding negative numbers.

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?

Think of it this way: adding a negative is like taking away or going backwards. On a number line, backwards means left, so $-4 + (-2)$ means start at -4 and go 2 steps backward (left).

How is this different from subtraction?

Great question! $-4 + (-2)$ and $-4 - 2$ give the same answer (-6) but think of addition as combining two negative values, while subtraction is taking away a positive value.

What if I get confused about which direction to move?

Use this trick: positive numbers move right (→), negative numbers move left (←). So adding (+3) means 3 steps right, adding (-3) means 3 steps left!

How do I remember that negative + negative = more negative?

Think about temperature! If it's -4°F and drops another 2 degrees, you get -6°F (colder). Negative + negative always gives a more negative result.

Can I just ignore the number line and do this in my head?

The number line helps you visualize the concept, but once you understand it, yes! Just remember: $-4 + (-2) = -(4 + 2) = -6$ . Add the numbers and keep the negative sign.

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