How do you use multiplying by 1 to find an expression equivalent to 20/11 with a denominator of 11x?

Dec 28, 2016

To maintain equivalency you must multiply by $\textcolor{red}{\frac{x}{x}} = 1$

Explanation:

First, we need to use our understanding that:

$\textcolor{red}{\frac{a}{a}} = 1$ where $\textcolor{red}{a}$ can be any term besides $0$ (you cannot divide by $0$).

Next to transform the denominator from $11$ to $11 x$ we must multiply $11$ by $x$. However, to keep equivalency we need to multiply this fraction by 1 or by, in this case:

$\textcolor{red}{\frac{x}{x}}$

$\frac{20}{11} \times \textcolor{red}{\frac{x}{x}} = \frac{20 \times \textcolor{red}{x}}{11 \times \textcolor{red}{x}} = \frac{20 \textcolor{red}{x}}{11 \textcolor{red}{x}}$