Solve 5+(-13): Adding Positive and Negative Numbers on a Number Line

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

Adding a negative number is the same as subtracting! Think of it like this: $ 5 + (-13) = 5 - 13 $. When you subtract a bigger number from a smaller one, you get a negative result.

Q: How do I know which direction to move on the number line?

Positive numbers move you right, and negative numbers move you left. Since we're adding -13, we move 13 spaces to the left from our starting position of 5.

Q: Can I solve this without using the number line?

Yes! You can think of it as $ 5 - 13 = -8 $. When subtracting a larger number from a smaller one, the answer is negative, and the value is the difference between the numbers.

Q: How do I remember the sign rules for adding integers?

Same signs: Add the numbers, keep the signDifferent signs: Subtract the smaller from the larger, use the sign of the larger numberIn $ 5 + (-13) $, we have different signs, so we get $ -(13-5) = -8 $.

Integer Addition with Negative Numbers

Solve the following expression using the number line below:

$5+(-13)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 According to the exercise, we'll start from point 5 on the positive side (right)

00:08 The number is directed and negative

00:13 The negative direction on the axis is to the left, so we'll go 13 left

00:27 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 expression using the number line below:

$5+(-13)=$

Step-by-step solution

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

Now let's deal with the operation in the exercise, given that the operation is $+(-13)$

Since the number minus 13 is less than 0, we will move thirteen steps to the left from the number 5, where each step represents one whole number as follows:

We can see that the number we reached is minus 8.

Final Answer

$-8$

Key Points to Remember

Essential concepts to master this topic

Direction Rule: Adding negative numbers means moving left on number line
Technique: Start at 5, move 13 steps left: 5 → 4 → 3 → 2 → 1 → 0 → -1 → -2 → -3 → -4 → -5 → -6 → -7 → -8
Check: Count positions from starting point: 5 to -8 is 13 steps left ✓

Common Mistakes

Avoid these frequent errors

Adding the absolute values instead of subtracting
Don't add $5 + 13 = 18$ when you see addition with negatives! This ignores the negative sign and gives a positive result instead of negative. Always recognize that adding a negative means subtracting and 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 answer smaller?

Adding a negative number is the same as subtracting! Think of it like this: $5 + (-13) = 5 - 13$ . When you subtract a bigger number from a smaller one, you get a negative result.

How do I know which direction to move on the number line?

Positive numbers move you right, and negative numbers move you left. Since we're adding -13, we move 13 spaces to the left from our starting position of 5.

What if I lose count while moving on the number line?

Break it into smaller steps! From 5, first move to 0 (that's 5 steps), then continue moving left 8 more steps to reach -8. Total: 5 + 8 = 13 steps.

Can I solve this without using the number line?

Yes! You can think of it as $5 - 13 = -8$ . When subtracting a larger number from a smaller one, the answer is negative, and the value is the difference between the numbers.

How do I remember the sign rules for adding integers?

Same signs: Add the numbers, keep the sign
Different signs: Subtract the smaller from the larger, use the sign of the larger number

In $5 + (-13)$ , we have different signs, so we get $-(13-5) = -8$ .

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