How many types of Integer Operatiions explain?
Adding Integers
The rules for adding integers are:
1. A positive number plus a positive number equals the sum of the two positive numbers.
2. A negative number plus a negative number equals the sum of their absolute values, with a negative sign.
3. To add a positive number and a negative number, take the absolute values of both integers. Subtract the smaller number from the bigger number. In the answer the resulting number will have the same sign of the integer whose absolute value is bigger.
Here are some sample problems involving addition:
a) 3 + 5 = 8
b)-3 + -5 = -8
c) 3 + -5 = -2
d) -3 + 5 = 2
Subtracting Integers
To subtract integers, change the problem to an addition problem by following these two rules:
1. Change the subtraction of a negative to the addition of a negative.
2. Convert two negative signs that occur next to each other to a positive sign.
Here are two example problems:
5-(-3) = 5+-(-3)=5+(+3)=5+3
-5-3 = -5+-3
For the first problem, follow rule number 1. The subtraction changes to addition and a negative sign is placed before the negative 3. Then, follow rule number 2. The two negative signs change to a positive, which leaves five plus positive 3, which is the same as 5 plus 3.
For the second problem, follow rule number 1. The subtraction changes to addition and a negative sign is placed before the 3. Now you have the addition of negative 3 and negative 5.
Once you change the subtraction problem into an addition problem, use the rules for addition to get the answer.
The answers to the example problems are 8 and -8.
Multiplication and Division
Multiplying integers and dividing integers follow the same steps.
1. Change both integers to positive numbers and multiply/divide.
2. The final answer should meet the following rules:
a. If the two numbers are positive the answer is positive.
b. If the two numbers are negative, the answer is positive.
c. If one number is positive and one number is negative, the answer is negative.
A way to remember this pattern is to think of positive as ‘good' and negative as ‘bad' and remember this saying:
"If a good thing happens to a good person, it's good.
If a bad thing happens to a bad person, it's good.
If a good thing happens to a bad person, it's bad.
If a bad thing happens to a good person, it's bad."
Here are sample multiplication/division problems:
8x2 = 16
-8 x-2 = 16
-8 /2 = -4
8/ -2 = -4
For the first problem, both numbers are positive, so the answer is positive 16.
For the second problem, multiply 8 and 2, to get 16. In the problem, both numbers are negative, so the answer is positive 16.
For the last two problems, divide 2 into 8 to get 4. In both these problems, one number is negative and one number is positive, so both answers are negative 4.