Solve 3 + (-4): Using Number Line to Add Negative Numbers

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

Adding a negative number is the same as subtracting a positive number! When you add (-4), you're really doing $ 3 - 4 $, which means moving 4 steps to the left from your starting position.

Q: How do I know which direction to move?

Look at the sign of the second number: positive numbers move right, negative numbers move left. The operation (+ or -) combined with the sign tells you the final direction.

Q: What if I start at a negative number?

The same rules apply! If you start at $ -2 $ and add $ (-3) $, move 3 steps left from -2 to reach -5. Always count from your starting position.

Q: Why is the answer negative when I started with a positive number?

Because you moved further left than your starting point! Starting at 3 and moving 4 steps left takes you past zero into negative territory. This is normal when the negative number has a larger absolute value.

Addition with Negative Integer Movement

Solve the following problem using the number line below:

$3+(-4)=$

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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, positive

00:07 Movement to the positive side of the axis is to the right

00:10 Therefore, from point 0 we'll take 3 jumps to the right

00:14 The number is directed, negative

00:18 Movement to the negative side of the axis is to the left

00:22 We'll take 4 jumps to the left

00:28 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:

$3+(-4)=$

Step-by-step solution

We will locate the number 3 on the number line, then move 4 steps to the left from it (since minus 4 is less than zero):

We can see that we have reached the number minus 1.

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding negative numbers means moving left on the number line
Technique: Start at 3, move 4 steps left to reach -1
Check: Count the steps from 3 to -1: 4 steps leftward ✓

Common Mistakes

Avoid these frequent errors

Moving right when adding negative numbers
Don't move right when adding (-4) = getting 7 instead of -1! Negative numbers always move left on the number line, regardless of whether you're adding them. Always remember: adding negative means moving left, subtracting negative means moving right.

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 is the same as subtracting a positive number! When you add (-4), you're really doing $3 - 4$ , which means moving 4 steps to the left from your starting position.

How do I know which direction to move?

Look at the sign of the second number: positive numbers move right, negative numbers move left. The operation (+ or -) combined with the sign tells you the final direction.

What if I start at a negative number?

The same rules apply! If you start at $-2$ and add $(-3)$ , move 3 steps left from -2 to reach -5. Always count from your starting position.

Can I use this method for bigger numbers?

Absolutely! The number line method works for any integers. For larger numbers, you might visualize the movements or use the rule: same signs add, different signs subtract.

Why is the answer negative when I started with a positive number?

Because you moved further left than your starting point! Starting at 3 and moving 4 steps left takes you past zero into negative territory. This is normal when the negative number has a larger absolute value.

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