Rules on Basic Operations of Integers
A. Addition
a>b
a
+
+
-
b
+
+
Operation
add
add
subtract
subtract
a+b
+
+
-
Operation
subtract
subtract
add
add
a-b
+
+
-
Operation
subtract
subtract
a-b
+
Examples:
1. 5 + 3 = (5+3) = 8
2. -5 + -3 = -(5+3) = -8
3. 5 + -3 = (5-3) = 2
4. -5 + 3 = -(5-3) = -2
B. Subtraction
a>b
a
+
+
-
b
+
+
a<b
a
+
-
b
+
-
Examples:
1. 5 – 3 = (5-3) = 2
2. -5 – -3 = -(5-3) = 2*
3. 5 – -3 = (5+3) = 8*
4. -5 – 3 = -(5+3) =8
5. 3 – 5 = -(5-3) = -2
6. -3 – -5 = (5-3) = 2*
* Note that “minus negative (– -)” means “add(+)”
Tip: To avoid confusion with rules for subtraction, memorize the rules for addition and
remember that minus is actually plus negative.
5 minus 3 is the same as 5 plus negative 3.
5 – 3 = 2 5 + -3 = 2
C. Multiplication
a
+
+
b
+
-
Operation
multiply
multiply
multiply
ab
+
+
-
In multiplication, regardless of which number is larger, the general rule is that the product of two
numbers with the same sign is always positive.
Example
1. 5 x 3 = 15
2. -5 x -3 = 15
3. -5 x 3 = -15
4. 5 x -3 = -15
D. Division
a
+
+
b
+
-
Operation
divide
divide
divide
ab
+
+
-
Similar with multiplication, the rules for division is the same since division is actually
multiplying one number by the reciprocal of the other. a/b = a(1/b)
Examples:
1. 15/3 = 5
2. -15/-3 = 5
3. -15/3 = -5
4. 15/-3 = -5
E. Operations with 0.
a. 0 + x = x
x+0=x
Adding a number to zero and adding zero to a number will have the number as the answer.
0+3=3
3+0=3
b. 0 – x = -x
x–0=x
Subtracting a number from zero will yield a negative answer. However, subtracting zero from a
number will yield the original number.
0 – 3 = -3
3–0=3
c. (x)(0) = 0
(0)(x) = 0
All numbers multiplied by or to zero is always equal to zero.
3x0=0
0x3=0
d. 0/x =0
x/0 = undefined
Dividing zero will always yield zero. However, dividing a number by zero is a mathematical
error and undefined.
0/3 =0
3/0 = undefined