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How to add integers

I would love to help you master adding integers. Before we dive into the math, I want to make sure I tailor this session perfectly for you.

Could you let me know if you are currently studying this in school, or are you learning it for another reason? Also, are you already comfortable with basic addition of positive numbers?

Studying for school, and I'm comfortable with basic addition

That's great! Since you've already got a solid grip on basic addition, we can jump right in. Let's start with a clear picture of what we're working with: are simply whole numbers that can be positive, negative, or zero.

Your path
Adding Integers with Different Signs
Practice and Application

To visualize how these numbers behave, it's best to look at a number line. Moving to the right increases our value (addition of positives), while moving to the left decreases it. Let's see how this works visually.

A horizontal number line ranging from -5 to 5, centered on 0, with a blue position marker highlighting the integer +3.

When we add integers, we are essentially taking a starting point on this line and moving left or right. Ready to see what happens when we combine positive and negative steps?

Continue to basic rules for same-sign integers

Let's dive right into our first rule for combining integers with the same sign: adding two positive numbers together.

Rule 1: Adding Two Positive Integers

When you add two positive integers, you're doing the exact same standard addition you've been doing for years. You simply add their values together, and the answer stays positive. On our number line, this is like starting at a positive number and continuing to walk further to the right. Let's look at a simple example: 3+2=53 + 2 = 5 Because both numbers are positive, we start at 33 and move 22 units to the right, landing at positive 55.

Rule 2: Adding Two Negative Integers

Now, what happens if both numbers are negative? The rule is actually very similar: you add their together, and then you keep the negative sign. Think of it like accumulating debt. If you owe a friend $3, and then you borrow another $2, you now owe them $5 altogether. Mathematically, we write this as: −3+(−2)=−5-3 + (-2) = -5 On the number line, we start at −3-3 and move 22 units to the left (the negative direction), which lands us right at −5-5.