Multiplicative Identity

The multiplicative identity is the number 1.

Multiplying any natural number, integer, or real number (n) by 1 leaves the number unchanged.

$$ n \cdot 1 = 1 \cdot n = n $$

The result is the same regardless of whether 1 appears as the first or the second factor.

For example

$$ 5 \cdot 1 = 5 $$

$$ 1 \cdot 5 = 5 $$

Several properties of division follow directly from the multiplicative identity, since division is the inverse operation of multiplication.

• If the divisor is equal to 1, the quotient is equal to the dividend (n = q). $$ \frac{n}{1} = q \ \ \text{because} \ \ n = q \cdot 1 $$

  For example $$ \frac{5}{1} = 5 \ \ \text{because} \ \ 5 = 5 \cdot 1 $$

• If the quotient is equal to 1, the dividend and the divisor are equal (n = m). $$ \frac{n}{m} = 1 \ \ \text{because} \ \ n = m \cdot 1 $$

  For example $$ \frac{5}{5} = 1 \ \ \text{because} \ \ 5 = 5 \cdot 1 $$

And so on.