integers: When adding integers, negatives and positives can be
switched to make questions simpler.For example: 3+(-2) = 3–2 = 1. Before switching negatives with positives, always make sure the negative number is second. For
example: (-7)+6 = 6+(-7) = 6-7 = (-1).
negatives: When subtracting integers, two negatives always
make a positive when you are subtracting. For example: 5-(-6) = 5+6 = 11. But when both integers
are negative, only the second integer should become a positive. For example: (-5)-(-4)= (-5)+4= (-1). The two last
negatives make them positives.
integers: When multiplying integers, if the integers are both
different (one is negative and one is positive) then the product is negative. And if they are both positive or negative
then the product becomes positive.
Dividing integers: This is the exact same thing as multiplying integers, if the integers
are both different (one is negative and one is positive) then the product is negative. And again if they are both positive
or negative then the product becomes positive.
Integers as Exponents: When multiplying a positive integer by a negative exponent,
first make the number into a fraction. E.g. 4^(-2) = 4/1^(-2). Now multiply
as if the integer were positive. E.g. 4/1^(-2) = 4/1^2 = 16/1. To finish, invert
the fraction. E.g. 16/1 = 1/16.
When multiplying negative numbers by positive exponents, multiply as if the integer was positive. If the exponent is even, the product remains positive.
If the exponent is odd, the product becomes negative.
For example: (-3)^4=81 (-3)^(-4)=(-81)