So you think multiplying and dividing positive and negative integers is complicated... Don't stress! I'll show you how to make sense of this important math topic. Let's start with multiplication.
Multiplying positive Integers
Imagine that you stand at a highway intersection. Cars are going east and west. Instead of a compass you can also use a number line, where east is the positive direction and west is the negative direction.
A blue car starts at your standing point, driving east, in a positive direction on the number line, going fifty miles per hour. After one hour, the blue car is here, fifty miles east of where you stand. And after two hours, the car is 100 miles east, at positive 100 on the number line.
Let's write this as an equation. Going for two hours 50 miles per hour in the positive direction can be written as 2 · 50 = 100. What happens if a car travels in the opposite direction? Let's go back to where you stand.
Multiplying negative Integers
Imagine, now, that a red car is going west, in a negative direction on the number line. Two hours later, the red car is 100 miles west of where you stand, at negative 100. I'll write this as a number sentence. Remember, going west in this case means going 50 miles per hour in negative direction. So we have 2 · −50 = −100.
Now, let's think about this topic another way. Where was a car going east two hours before it passed you standing at the intersection? Two hours before, driving east at fifty miles per hours, this car was one hundred miles west of where you stand, at minus 100 on the number line.
Let's write this as an equation. Two hours ago can be written as negative two. Remember, going east at fifty miles per hour means going in positive direction. So the equation is: −2 · 50 = −100.
And what about a car traveling west? Where was it two hours before? Traveling at fifty miles per hour in a negative direction on the number line, it was 100 miles east of where you stand. This is equal to positive 100.
I'll show you the equation. Negative two, which represents 2 hours ago, times negative fifty - for going 50 miles west, in the negative direction - is equal to positive one hundred: −2 · −50 = 100.
Rule for Multiplication and Division
Here's a cheat sheet of our equations. This equation is for going east in positive direction for two hours: two times fifty equals one hundred. This one shows going west in negative direction for two hours: 2 · −50 = −100. Here we look at where the car going east in positive direction was 2 hours ago: −2 · 50 = −100. And this shows where the car going west in negative direction was 2 hours ago: −2 · −50 = 100.
Can you find a pattern? You see here:
- If you multiply two positive numbers, you get a positive product
- If you multiply a postive with a negative you get a negative answer and
- If you multiply a negative with a positive, you also get a negative
- But if you multiply two negatives, you will get a positive product
Lets rearrange the equations. So now you have a rule: Multiplying like signs will give you a positive product and multiplying unlike signs will give a negative answer.
You know what's so great about this rule? It works the same for multiplying and dividing numbers! And, not just integers but fractions, too.
Hooray! With this simple rule, you can be the master of multiplying and dividing positive and negative numbers! But remember, you should never mess with the Space Time Continuum.
Стоя на ковре возле письменного стола, она в растерянности осматривала кабинет шефа. Комнату освещали лишь странные оранжевые блики. В воздухе пахло жженой пластмассой.