How To Add Subtract Multiply And Divide Integers

Last week, my friend Dave tried to settle a bar tab by calculating “negative drinks.” He owed me three, but he’d bought me two. “So I owe you… negative one?” he said, grinning. I had to explain that no, a negative drink would mean I owe you, and that math doesn’t care about your hangover.

That’s the thing about integers—they’re just numbers with attitudes. They can be positive, negative, or zero, and they follow rules that sometimes feel like a grumpy landlord’s lease. But once you get it, you’ll never look at a thermometer the same way again.

Adding Integers: The Elevator Trick

Think of a number line as an elevator. Positive numbers are floors above ground, negatives are basement levels. Adding a positive? Go up. Adding a negative? Go down.

So, 5 + (-3) means start at floor 5, then ride down 3 floors. You land on 2. Easy, right? But what about -4 + (-2)? You start in the basement at -4, then go down two more. That’s -6. (Hope you brought a flashlight.)

The secret: if signs are the same, add the numbers and keep the sign. If different, subtract the smaller from the bigger—and the answer takes the sign of the bigger number. Boom. No elevator music required.

Subtracting Integers: The Double Negative Dance

Subtracting is where people get twitchy. Here’s the trick: subtracting a number is the same as adding its opposite. Yes, it’s a cheat code. Use it.

Take 7 - (-2). That’s 7 plus 2, because subtracting a negative is like saying “remove that debt.” So 7 - (-2) = 9. Your brain might scream “two negatives make a positive!” and it’s right, but only because we’re turning subtraction into addition.

Add, Subtract, Multiply, and Divide with Positive and Negative Integers

For -3 - 4, rewrite as -3 + (-4) = -7. You’re starting negative and going even more negative. It’s like getting a parking ticket when you’re already broke. (I feel you.)

Multiplying Integers: The Friendship Rule

Multiplication is simpler, but it has a bouncer at the door: the sign rule. Same signs? Positive. Different signs? Negative. That’s it.

So 3 × 5 = 15 (both positive, happy friends). (-3) × 5 = -15 (one negative, one positive—they argue). (-3) × (-5) = 15 (two negatives? They become besties and make a positive). Think of it like a party: two grumpy people cancel each other out and suddenly everyone’s dancing.

Why does this work? Because multiplying by a negative flips the direction on the number line. Multiply two negatives, and you flip twice—back to positive. Math is weirdly optimistic sometimes.

Dividing Integers: Same Party, New DJ

Division uses the exact same sign rules as multiplication. Same signs produce a positive quotient; different signs give a negative one. No exceptions.

Adding Integers Steps

15 ÷ 3 = 5. (-15) ÷ 3 = -5. 15 ÷ (-3) = -5. (-15) ÷ (-3) = 5. Boring? Maybe. Consistent? Absolutely. Just remember: you cannot divide by zero. That’s not a rule—that’s a math apocalypse. Zero as a divisor breaks the universe. Don’t do it.

One more thing: when dividing integers, the result might not be an integer. For example, 7 ÷ 2 gives 3.5, which is not an integer. If the problem says “divide integers,” they usually want an integer answer—so you’ll need to round, truncate, or accept that sometimes life gives you fractions. (Blame the algorithm, not me.)

Putting It All Together: Your Integer Survival Kit

Here’s your cheat sheet. For addition, use the elevator. For subtraction, add the opposite. For multiplication and division, check the bouncer: same signs = positive, different signs = negative.

Practice with real-world stuff: a $5 coffee order with a $3 coupon is 5 + (-3) = $2. A temperature drop of 8 degrees from -2°C is -2 - 8 = -10°C. You’re using integers every time you overdraft your bank account or check the weather. (See? Math is personal.)

Dave eventually paid his tab—after I showed him his “negative drinks” actually meant he owed me five more. He didn’t laugh, but I did. Integers are honest, even when your friends aren’t. So go forth, add, subtract, multiply, and divide with confidence. And if you ever get stuck, just remember: two negatives make a positive, and one positive joke makes a whole article.