# How do you use multiplying by 1 to find an expression equivalent to 7/6 with a denominator of 6d?

Dec 31, 2016

$\frac{7}{6} \times \frac{d}{d} = \frac{7 d}{6 d}$

#### Explanation:

The answer to this question is a lot easier than it looks at first glance!

Remember that $1$ can be written in many different forms.

As a fraction, when the numerator and the denominator are the same, the fraction is equivalent to 1.

$\frac{8}{8} = 1 \text{ and "(-11)/(-11) = 1" and "x/x = 1" and } \frac{d}{d} = 1$

Remember that $\frac{0}{0}$ is undefined.

To make any equivalent fraction multiplying by 1 does not change the value of the fraction, but changes what it looks like.
Just multiply the top and bottom by the same number!

e.g.$\text{ "2/3 xx color(red)(5/5) = 10/15" } \leftarrow \textcolor{red}{\frac{5}{5} = 1}$

In this case we have to find a fraction equivalent to $\frac{7}{6}$, but the denominator is specified.

$\frac{7}{6} \times \frac{d}{d} = \frac{7 d}{6 d} \text{ } \leftarrow d \ne 0$