Multiplying any number by zero always equals zero. Below are some examples.
To see why multiplying any number by zero always equals zero, let's take a look at the multiplication table for , shown below.
As we go down the list, the number in blue is reduced by each time. Following this pattern, we must have .
Note that, since multiplication is commutative, multiplying zero by any number (including itself) equals zero as well. Some examples are shown below.
What is the value of
Multiplying any number by zero always gives zero. Therefore,
Calculate the value of $1\,255 \cdot 0.$
|
a
|
$-1\,255$ |
|
b
|
$0$ |
|
c
|
$125$ |
|
d
|
$1\,255$ |
|
e
|
$\dfrac{1}{125}$ |
Calculate the value of $15 \cdot 0.$
|
a
|
$15$ |
|
b
|
$-15$ |
|
c
|
$0$ |
|
d
|
$150$ |
|
e
|
$\dfrac{1}{5}$ |
Dividing zero by any number (other than zero) always equals zero. For example:
To understand why dividing zero by any number (other than zero) always equals zero, think about it this way: if you have zero pizzas, and you want to divide zero pizzas among ten friends, then each friend will get exactly zero pizza.
Calculate the value of
Zero divided by any number (other than zero) equals zero. Therefore,
$0\div16=$
|
a
|
$0$ |
|
b
|
$-16$ |
|
c
|
$\dfrac{1}{16}$ |
|
d
|
$16$ |
|
e
|
$\dfrac{1}{6}$ |
Compute the value of
Zero divided by any number (other than zero) equals zero. Therefore,
Calculate the value of $0\div\dfrac{3}{4}.$
|
a
|
$\dfrac{4}{3}$ |
|
b
|
Undefined |
|
c
|
$-\dfrac{3}{4}$ |
|
d
|
$0$ |
|
e
|
$4$ |
Compute the value of $0\div\dfrac{3}{5}.$
|
a
|
$3.5$ |
|
b
|
$0$ |
|
c
|
Undefined |
|
d
|
$-\dfrac{3}{5}$ |
|
e
|
$\dfrac{5}{3}$ |
Division by zero is undefined. No number can be divided by zero, not even zero itself.
To see why, notice that if we divide by we get
Therefore, by the relationship between multiplication and division, we have
However, this argument does not work if we divide by zero. Suppose we have
Then, by the relationship between multiplication and division, we have
and this relationship cannot be true because any number multiplied by zero is zero! Therefore, is not a number.
What is
We cannot divide any number by zero. Therefore, is undefined.
$45\div0=$
|
a
|
$-\dfrac{1}{45}$ |
|
b
|
$\dfrac{0}{45}$ |
|
c
|
Undefined |
|
d
|
$45$ |
|
e
|
$0$ |
What is $1\div0?$
|
a
|
$1$ |
|
b
|
Undefined |
|
c
|
$-1$ |
|
d
|
$\dfrac{0}{1}$ |
|
e
|
$0$ |