Negative Numbers

Negative numbers are the opposite of positive numbers and come before the number 0. For example, the opposite of 4 is -4. When looking at the number line below, you can see the numbers to the left of 0 have a (-) in front of them. This represents that they are negative numbers.

Adding and subtracting negative numbers is different than when adding and subtracting positive numbers.

When adding positive numbers, the sum is bigger. (4 + 5 = 9). When adding negatives the sum is smaller ( -4 + -5 = -9). Adding negatives is similar to subtracting because

When subtracting positive numbers, the difference is smaller. When subtracting negative numbers, it varies. When a smaller negative number is subtracted from a larger negative, the difference ends up being a larger number, usually positive. For example, -2 - (-4) = 2. The negative number (-2) is smaller. When subtracting a negative number (-4), the double negative makes the problem an addition. Making it possible for the answer to be a larger number rather than a smaller number. -2-(-4)= -2+4=2

When multiplying a negative number by a positive number, the product is negative ( -2 * 5 = -10).

When a negative number is multiplied by a negative number, the product is actually positive, ( -2 * -5 = 10). This occurs when the two negatives are multiplied, the negative symbols (-) come together and form a positive symbol (+), making the answer positive. This does not occur when multiplying a negative by a positive as there is one negative symbol (-) and can not form a positive symbol.

When dealing with negative numbers in inequalities, say that the equation is -3x>6.  To solve this one would have to divide by negative three, which makes sense, but when you do so, the sign of the inequality has to be switched around thus making is x<-2.