How to Add Integers (Rules & Examples)

Question

Adding integers is a fundamental arithmetic operation that combines two or more integers to find their sum. Integers are whole numbers (not fractions) that can be positive, negative, or zero. Understanding the rules for adding integers is crucial for various mathematical concepts and real-world applications. This guide will explain the rules and provide examples to help you master integer addition.

BrianGriffin · Accepted Answer

Hey there! 👋 It's totally common to get a bit tangled up with positive and negative numbers. But don't worry, adding integers is quite straightforward once you get the hang of a couple of key rules. Let's break it down step-by-step!

First off, remember that integers are all whole numbers (positive, negative, and zero), like $... -3, -2, -1, 0, 1, 2, 3 ...$.

Rule 1: Adding Integers with the Same Signs
This is the easiest one! If both integers have the same sign (both positive or both negative), here's what you do:

Add their absolute values (ignore the signs for a moment).
    Keep the common sign in your answer.

Examples:
Both Positive:
Let's add $3$ and $5$. Both are positive.
1. Add their absolute values: $|3| + |5| = 3 + 5 = 8$.
2. Keep the common sign (positive).
So, $3 + 5 = 8$. 🎉

Both Negative:
Let's add $-3$ and $-5$. Both are negative.
1. Add their absolute values: $|-3| + |-5| = 3 + 5 = 8$.
2. Keep the common sign (negative).
So, $-3 + (-5) = -8$. (Think of it as owing $3 and then owing another $5 – now you owe a total of $8.)

Rule 2: Adding Integers with Different Signs
This is where most people get confused, but it's not too bad. If the integers have different signs (one positive and one negative), follow these steps:

Subtract the smaller absolute value from the larger absolute value.
    The answer will have the sign of the number with the larger absolute value.

Examples:
Positive + Negative:
Let's add $7$ and $-3$.
1. Find absolute values: $|7| = 7$ and $|-3| = 3$.
2. Subtract the smaller absolute value from the larger: $7 - 3 = 4$.
3. The number with the larger absolute value is $7$ (which is positive), so the answer is positive.
So, $7 + (-3) = 4$. (Imagine you have $7 and you spend $3 – you're left with $4.)

Negative + Positive:
Let's add $-10$ and $4$.
1. Find absolute values: $|-10| = 10$ and $|4| = 4$.
2. Subtract the smaller absolute value from the larger: $10 - 4 = 6$.
3. The number with the larger absolute value is $-10$ (which is negative), so the answer is negative.
So, $-10 + 4 = -6$. (You owe $10 and you pay back $4 – you still owe $6.)

Adding Zero
This is a super simple one: Adding zero to any integer doesn't change its value. Easy peasy! 😉

$5 + 0 = 5$
    $-12 + 0 = -12$

And that's pretty much it! Practice makes perfect, so try a few more problems. You've got this! 💪

How to Add Integers (Rules & Examples)

1 Answers

Rule 1: Adding Integers with the Same Signs

Rule 2: Adding Integers with Different Signs

Adding Zero

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