Study Guide

Basic Operations - Multiplying and Dividing Integers

Multiplying and Dividing Integers

You've made it past addition and subtraction. Guess what's next? It's time to learn the ropes of multiplying and dividing integers.

The rules for multiplication and division are exactly the same: multiply and divide the numbers as normal. If the signs are the same, the answer is positive. If the signs are different, the answer is negative.

Let's say we're playing catch with some buddies and the guy with the ball yells, "Go long, go long!" We take 3 steps backwards (in the negative direction) and, realizing that's not enough, we do that a total of 4 times. We will have taken 12 steps backwards, ending up deep in the negative zone.

In math-speak we could write this as:

(-3) × 4 = -12

Or:

4 × (-3) = -12

Either way, it's the same answer. A negative times a positive (or a positive times a negative) has an answer deep in the negative zone.

Now a friend joins the game who has never played catch before (seriously?). As we line up facing the guy with the ball and he yells, "Go long," the new player turns around facing away from the thrower and takes 3 steps backward. He does that 4 times. He's certainly traveling backwards, but because he also turned around, he's actually traveling toward the thrower. He's moving in the positive direction.

(-3) × (-4) = 12

A negative times a negative has an answer back in the positive zone.

Here are the rules:

Positive(×) or (÷)positive=positive
Positive(×) or (÷)negative=negative
Negative(×) or (÷)positive=negative
Negative(×) or (÷)negative=positive

Yep, two wrongs (negatives) actually do make a right (positive)...at least when we're multiplying or dividing.

Batman and the Joker

Think of someone you consider to be a good guy (like Batman) and someone who is a bad guy (like the Joker). Next, ask these questions:

  1. If something good (+) happens to someone good (+): is that good or bad, like Batman winning the lottery? 
    • Good (+)
  2. If something good (+) happens to someone bad (-): is that good or bad, like the Joker winning the lottery? 
    • Bad (-)
  3. If something bad (-) happens to someone good (+): is that good or bad, like Batman being captured?
    • Bad (-)
  4. If something bad (-) happens to someone bad (-): is that good or bad, like the Joker being captured? 
    • Good (+)

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