Solve 5 + (-2): Step-by-Step Number Line Solution

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

Adding a negative number is the same as subtracting a positive number. When you add $ +(-2) $, you're really doing $ 5 - 2 = 3 $.

Q: Which direction do I move on the number line?

Right for positive, left for negative! Since we're adding $ -2 $, move 2 steps to the left from 5.

Q: What if I get confused by the double signs?

Remember: same signs add, different signs subtract. Since $ + $ and $ - $ are different, you subtract: $ 5 + (-2) = 5 - 2 = 3 $.

Q: Is there an easier way than using the number line?

Yes! Convert $ 5 + (-2) $ to $ 5 - 2 $ and solve normally. The number line helps you visualize why this works.

Q: What if the negative number was bigger than the positive?

Like $ 3 + (-5) $? You'd get a negative answer: $ 3 - 5 = -2 $. Start at 3, move 5 steps left, land on -2.

Integer Addition with Negative Numbers

$5+(-2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 The number is directed, and positive

00:13 The positive direction on the axis is rightward, so we'll take 5 to the right

00:17 The number is directed, and negative

00:21 The negative direction on the axis is leftward, so we'll take 2 to the left

00:31 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

$5+(-2)=$

Step-by-step solution

Let's locate the number 5 on the number line.

Since the number 5 is greater than 0, we will move five 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 $+(-2)$

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

We can see that the number we reached is 3.

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding negative numbers means moving left on number line
Technique: Start at 5, move 2 steps left: 5 + (-2) = 3
Check: Verify by counting: 5 → 4 → 3 lands on 3 ✓

Common Mistakes

Avoid these frequent errors

Treating +(-2) as regular addition
Don't add 5 + 2 = 7 when you see +(-2)! The parentheses around -2 mean you're adding a negative number, which moves left on the number line. Always recognize that +(-2) means subtract 2.

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 a positive number. When you add $+(-2)$ , you're really doing $5 - 2 = 3$ .

Which direction do I move on the number line?

Right for positive, left for negative! Since we're adding $-2$ , move 2 steps to the left from 5.

What if I get confused by the double signs?

Remember: same signs add, different signs subtract. Since $+$ and $-$ are different, you subtract: $5 + (-2) = 5 - 2 = 3$ .

Is there an easier way than using the number line?

Yes! Convert $5 + (-2)$ to $5 - 2$ and solve normally. The number line helps you visualize why this works.

What if the negative number was bigger than the positive?

Like $3 + (-5)$ ? You'd get a negative answer: $3 - 5 = -2$ . Start at 3, move 5 steps left, land on -2.

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