**Multiplication, Division, Addition, and Subtraction of Integers**

**Integers**

Positive and Negative Numbers

Positive and Negative Numbers

Addition with Positive Integers

You add positive integers every day.

For instance:

2 cars are in the driveway. 3 more are coming around the bend. How many cars is that? Oh yea, 5.

Simple.

Addition with Negative Integers

Addition with negative integers is exactly the same as with positive integers, but your answer will always be negative.

For instance:

-7 + (-4) = -11

is the same as

7 + 4 = 11

but the answer is negative.

Subtraction with Positive Numbers

This is done every day.

8 - 3 = 5

7 - 9 = -2

13 - 17 = -4

There are two different kinds of integers (whole numbers). The first kind are made up of numbers we use every day-- positive numbers. The second kind are numbers that are that are lesser used-- negative numbers.

Positive numbers are to the right of the zero on a classic, left-to-right number line. Negative numbers are on the left. poop.

Addition with Positive and Negative Numbers

Addition with positives and negatives is a bit more complicated. When you are adding positives and negatives, the sign of the bigger number in the equation will be the sign of the answer.

For instance:

-17 + 5

In this equation -17 is the bigger number. -17 is negative so we now know that the answer will be negative.

-17 + 5 = -12

Subtraction with Negative Numbers

This is slightly more difficult. For subtraction, there is one main principle: Keep-Change-Change.

Observe:

-5 - (-4)

k c c

-5 + 4 = -1

Subtraction with Positive and Negative Numbers

When subtracting with positive and negative numbers, you should use the k-c-c method as well.

For instance:

8 - (-5)

k c c

8 + 5 = 13

Or

-4 - 3

k c c

-4 + -3 = -7

Multiplication with Positive Numbers

Everyday multiplication is simple stuff.

For instance:

5 x 3 = 15

6 x 7 = 42

Multiplication with Negative Numbers

One might think that

a negative x a negative = a negative

but it is actually a positive. The rule for multiplication is if the signs are the same in the equation then the answer is positive and vice versa.

For instance:

-5 x -6 = 30

Or

-8 x -2 = 16

Multiplication with Positive and Negative Numbers

Remember: if the signs are different, the answer will be negative.

For instance:

-5 x 4 = -20

Or

9 x -3 = -27

Division with Negative Numbers

Remember that the same rule that applies to multiplication applies to division. If the signs are the same the answer will be positive.

For instance:

-10 / -5 = 2

Or

-9 / -3 = 3

Division with Positive Numbers

Remember: If the signs are the same the answer will be positive.

For instance:

12 / 6 = 2

Or

25 / 5 = 5

Division with Positive and Negative Numbers

Remember: If the signs are different, the answer will be negative.

For instance:

15 / -5 = -3

Or

-54 / 2 = -27