# Is 9/9 equal to 1 of 0.(9)?

## I don't know because 1/9 = 0.(1), so ... can 9/9 be 0.(9)

Jul 28, 2017

$\frac{9}{9} = 1$

#### Explanation:

Any number divided by itself equals 1. So $\frac{9}{9} = 1$. It's important to know this so that when you are adding or subtracting fractions with unlike denominators, you will be able to multiply the fractions by equivalent fractions in order to make the denominators equal without changing the value of the fraction. An equivalent fraction has the same numerator and denominator, and therefore is equal to $1$, like $\frac{9}{9}$.

Example:

$\frac{3}{5} + \frac{2}{10}$

Multiply $\frac{3}{5}$ by the equivalent fraction $\frac{\textcolor{red}{2}}{\textcolor{red}{2}}$.

$\frac{3}{5} \times \frac{\textcolor{red}{2}}{\textcolor{red}{2}} = \frac{6}{10}$ $\leftarrow$ $\frac{\textcolor{red}{2}}{\textcolor{red}{2}} = 1$

$\frac{6}{10} + \frac{2}{10} = \frac{8}{10}$

Jul 28, 2017

Either. You have found one of the proofs that $0. \left(9\right) = 1$

#### Explanation:

I am not used to the parentheses to indicate repeated decimals. I am more familiar with the "bar" notation

$0. \overline{9}$

Regardless of how we denote repeated digits,

$\frac{1}{9} = 0. \left(1\right) = 0. \overline{1}$

$\frac{1}{3} = \frac{3}{9} = 0. \left(3\right) = 0. \overline{3}$

and

$\frac{9}{9} = 0. \left(9\right) = 0. \overline{9}$, but also $\frac{9}{9} = 1$

so

$0. \left(9\right) = 0. \overline{9} = 1$