Solve 7+(-3): Adding Positive and Negative Numbers on a Number Line

Q: Why does adding a negative number make the result smaller?

Adding a negative number is the same as subtracting! So $ 7 + (-3) $ equals $ 7 - 3 = 4 $. Think of it as taking away 3 from 7.

Q: Which direction do I move for positive and negative numbers?

Positive numbers: Move right on the number lineNegative numbers: Move left on the number lineRemember: right is positive, left is negative!

Q: How do I know how many steps to take?

The number tells you how many steps! For $ +(-3) $, you take 3 steps to the left. The size of the number (ignoring the sign) is your step count.

Q: Can I just ignore the parentheses around -3?

No! The parentheses show that you're adding a negative number. $ 7 + (-3) $ is different from $ 7 - 3 $ in how it's written, but they give the same answer of 4.

Number Line Addition with Negative Numbers

$7+(-3)=$

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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 directed and positive

00:08 The positive direction on the axis is to the right, so we'll take 7 to the right

00:18 The number is directed and negative

00:23 The negative direction on the axis is to the left, so we'll take 3 to the 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

Understand the problem

$7+(-3)=$

Step-by-step solution

Let's locate the number 7 on the number line.

Since the number 7 is greater than 0, we will move seven steps to the right 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 the number minus 3 is less than 0, we will move three steps to the left from the number 7, where each step represents one whole number as follows:

We can see that the number we reached is 4.

Final Answer

$4$

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 7, move 3 steps left: 7 → 6 → 5 → 4
Check: Verify 7 + (-3) = 4 by counting steps: right 7, then left 3 ✓

Common Mistakes

Avoid these frequent errors

Moving in the wrong direction for negative numbers
Don't move right when adding a negative number like +(-3) = moving right 3 steps! This gives 7 + 3 = 10 instead of the correct answer. Always remember: adding negative means moving 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 a negative number make the result smaller?

Adding a negative number is the same as subtracting! So $7 + (-3)$ equals $7 - 3 = 4$ . Think of it as taking away 3 from 7.

Which direction do I move for positive and negative numbers?

Positive numbers: Move right on the number line
Negative numbers: Move left on the number line
Remember: right is positive, left is negative!

How do I know how many steps to take?

The number tells you how many steps! For $+(-3)$ , you take 3 steps to the left. The size of the number (ignoring the sign) is your step count.

What if I start from a different number than 7?

The process is exactly the same! Always start from your first number, then move the correct direction and distance based on what you're adding. The number line method works for any starting point.

Can I just ignore the parentheses around -3?

No! The parentheses show that you're adding a negative number. $7 + (-3)$ is different from $7 - 3$ in how it's written, but they give the same answer of 4.

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