Explaining how to add negative plus positive numbers can be a challenge for many teachers because the concept can seem confusing to students. However, understanding how to add positive and negative numbers is a crucial skill that lays the groundwork for success in math.
In this blog, we’ll carefully break down what happens when adding a negative and positive number, review the important rules, and provide simple, clear steps to make the process easier for students to grasp. Let’s dive in!
Understanding Positive and Negative Numbers
Before we jump into the addition of positive and negative numbers, it’s important to review what positive and negative numbers represent:
- Positive numbers are values greater than zero. They represent quantities like gains, increases, or moving forward.
- Negative numbers are values less than zero. They indicate losses, decreases, or moving backward.
Think of a number line, positive numbers lie to the right of zero, and negative numbers lie to the left. When we add numbers with different signs, we are essentially moving left or right along this line.
What is Negative Plus Positive?
Now, let’s define the basics! A negative plus a positive equals the difference between the two values, the sign of the result depends on which number has the larger absolute value.
Normally, addition means increasing a number’s value, but with integers, the outcome can either increase or decrease depending on the signs involved. Adding a negative number decreases the original value, while adding a positive number increases it.
This same rule applies whether you’re doing positive plus negative or negative plus positive — the process is exactly the same. You subtract the smaller absolute value from the larger one, then assign the sign of the number with the greater absolute value to the final answer.
For example:
-3 + 5 = 2 5 + (-3) = 2
Both calculations equal 2 because the positive number (5) has the larger absolute value.
How Do You Add Positive and Negative Numbers?
Many teachers wonder how to add negative and positive numbers in a way that actually makes sense to students. The good news is—it’s easier than it seems when you break it down into a few simple, logical steps:
Step 1: Think in Terms of Direction
When a negative number plus a positive number, think about a number line:
- Positive numbers move to the right ⟶
- Negative numbers move to the left ⟵
So when you add a negative to a positive, you’re really moving left from a starting point on the right.
For example: 7 + (–3), start at 7 and move 3 units left. You land at 4.
This kind of thinking builds strong mental math strategies and helps students visualize what’s really happening with signed numbers.
Step 2: Use Absolute Values to Simplify
Building on the direction concept, Step 2 focuses on absolute values to simplify addition. Here’s the clear step-by-step rule to follow:
- Ignore the signs and find the absolute value of each number.
- Subtract the smaller absolute value from the larger one.
- Assign the sign of the number with the larger absolute value to the result.
Example 1: 8 + (–5)
- Absolute values: 8 and 5
- Subtract: 8 – 5 = 3
- Since 8 (the positive number) is larger, the answer is +3
Example 2: (–9) + 4
- Absolute values: 9 and 4
- Subtract: 9 – 4 = 5
- Since 9 (the negative number) is larger, the answer is –5
Example 3: (–125) + 80
- Absolute values: 125 and 80
- Subtract: 125 – 80 = 45
- Since 125 (the negative number) has the larger absolute value, the answer is –45
These examples show that adding negatives and positives depends entirely on which number has the greater absolute value—not which comes first.
Step 3: Remember “The Bigger Number Wins”
When practicing negative plus positive problems, a student-friendly rule is: “Whichever number has the bigger absolute value gets to choose the sign.”
- If the negative number is larger in absolute value, your result will be negative.
- If the positive is larger, the answer will be positive.
This straightforward approach helps learners master the rules behind the addition of positive and negative integers, building a strong foundation for future operations involving integers, equations, and algebraic expressions.
Frequently Asked Questions
1. What is the rule for adding negative and positive numbers?
When adding positive and negative numbers, subtract the smaller absolute value from the larger one. The result takes the sign of the number with the larger absolute value.
For example: –4 + 7 = 3 (since 7 > 4, and 7 is positive, the result is positive)
2. Can positive and negative go together?
Yes, they absolutely can! In real-life and in math, we often combine positive and negative values—for example, gains and losses in money, temperatures above and below zero, or steps forward and backward.
Final Thoughts
Negative plus positive might sound confusing at first, but once students understand the rules and practice the steps, it becomes much easier. By practicing these strategies, students can gain confidence in adding positive and negative integers for more advanced math topics.
Want printable resources to reinforce this concept? Check out these positive and negative numbers worksheets to give your students hands-on practice that builds both skill and confidence!
