{{ option.icon }} {{ option.label }} arrow_right
{{ option.icon }} {{ option.label }} arrow_right
{{ option.icon }} {{ option.label }}
{{ option.icon }} {{ option.label }}
Division by Zero
tune
{{ topic.label }}
{{ result.displayTitle }}
{{ result.subject.displayTitle }}
navigate_next

# Division by zero

Consider the expression which shows dividing a number by zero. This division is considered undefined or not possible. This is because, there exists no number x, real or otherwise, such that
x0=5.
Division indicates how many times the denominator "fits" into the numerator. If you calculate to determine how many times 0 will fit in 5, you will never reach 5 no matter how many zeros you try.
Dividing by $0$ then becomes impossible.
Therefore, certain conditions must be specified when s denominator contains a variable. For example,

### Extra

An illustration

Another way to illustrate why division by 0 is undefined is to study the graph of By using a table of values some points on the curve can be found.

x =
-0.5 -2
-0.25 -4
-0.1 -10
0.1 10
0.25 4
0.5 2

Graphing the points on a coordinate plane allows the behavior of the function to be shown. The red points show what happens as x approaches 0 from the left, and the green points show what happens as x approaches 0 from the right.

The closer x comes to 0, on both sides, the more extreme the values of the functions become. The quotient approaches when x approaches 0 from the right, and when x approaches from the left. Because is a function, f can only produce one value when x=0. Therefore, division by 0 is undefined.

### Extra

The consequences of dividing by zero
Suppose dividing by zero was defined. Then, the "logic" below would be accepted as true. Let a and b be any real numbers/
a=b
ab=0
1=0

Since both sides of the equation are divided by ab=0, and ab=0, the expression was validly manipulated to create a false statement.

Community