To get rid of a fraction, we multiply by the reciprocal. So we take \(\displaystyle \frac{3}{5}x=9\) and multiply both sides by \(\displaystyle \frac{5}{}3}\):

\(\displaystyle \frac{3}{5}x=9\)

\(\displaystyle \frac{5}{3}*\frac{3}{5}x=9*\frac{5}{3}\)

Notice that \(\displaystyle \frac{5}{}3}\) and \(\displaystyle \frac{3}{5}\) cancel out, leaving us with \(\displaystyle x=9*\frac{5}{3}\).

At this point, you can either plug \(\displaystyle 9*\frac{5}{3}\) into your calculator, or you can solve this in pieces. 

We can do some manipulation to get: \(\displaystyle 9*\frac{5}{3}=\frac{9*5}{3}=\frac{9}{3}*5\)

\(\displaystyle \frac{9}{3}=3\), so we can plug that into \(\displaystyle x=\frac{9}{3}*5\).

\(\displaystyle x=\frac{9}{3}*5\)

\(\displaystyle x=3*5=15\)

To get rid of a fraction, we multiply by the reciprocal, so we take \(\displaystyle \frac{1}{3}x=7\) and multiply both sides by \(\displaystyle \frac{3}{1}\):

\(\displaystyle \frac{1}{3}x=7\)

\(\displaystyle \frac{3}{1}*\frac{1}{3}x=7*\frac{3}{1}\)

Since \(\displaystyle \frac{3}{1}*\frac{1}{3}=1\), we can simplify that equation to \(\displaystyle x=7*\frac{3}{1}\).

Therefore, \(\displaystyle x=7*3=21\).

To get rid of a fraction, we multiply by the reciprocal. So we take \(\displaystyle \frac{1}{9}x=4\) and multiply both sides by \(\displaystyle \frac{9}{1}\):

\(\displaystyle \frac{1}{9}x=4\)

\(\displaystyle \frac{9}{1}*\frac{1}{9}x=4*\frac{9}{1}\)

Since \(\displaystyle \frac{9}{1}*\frac{1}{9}=1\), we can simplify that equation to \(\displaystyle x=4*\frac{9}{1}\).

Therefore, \(\displaystyle x=4*9=36\).

To get rid of the \(\displaystyle \frac{x}{4}\), we multiply both sides by \(\displaystyle 4\):

\(\displaystyle \frac{x}{4}=2\)

\(\displaystyle 4*\frac{x}{4}=2*4\)

\(\displaystyle x=2*4\)

\(\displaystyle x=8\)

To solve this problem we need to reduce \(\displaystyle x=\frac{8}{2}\). Both the top and the bottom of \(\displaystyle \frac{8}{2}\) are divisible by \(\displaystyle 2\), so we can reduce it to \(\displaystyle \frac{4}{1}\). Anything divided by \(\displaystyle 1\) is itself, so \(\displaystyle x=\frac{8}{2}\) is the same as \(\displaystyle x=4\).

To solve, multiply the right side: 

\(\displaystyle x=9*\frac{2}{3}\)

\(\displaystyle x=\frac{18}{3}\)

\(\displaystyle x=6\)

To solve this problem, multiply across: \(\displaystyle x=13*\frac{1}{2}=\frac{13}{1}*\frac{1}{2}=\frac{13}{2}\).

\(\displaystyle 13\) is a prime number, so we cannot reduce further. From here, covert \(\displaystyle \frac{13}{2}\) into a mixed fraction: \(\displaystyle x=6\tfrac{1}{2}\)

To solve this problem, multiply across:

\(\displaystyle x=14*\frac{3}{2}=\frac{14}{1}*\frac{3}{2}=\frac{42}{2}= 21\)

\(\displaystyle x=9*\frac{2}{3}\)

\(\displaystyle x=\frac{9}{1}*\frac{2}{3}\)

\(\displaystyle x=\frac{9*2}{1*3}\)

\(\displaystyle x=\frac{18}{3}\)

\(\displaystyle x=6\)

To solve for \(\displaystyle x\), we need to isolate our variable. That means that we want ONLY the \(\displaystyle x\) on the left side of the equation.

\(\displaystyle x*\frac{2}{3}=12\)

We want to divide by \(\displaystyle \frac{2}{3}\). The way you divide by a fraction is to multiply by the reciprocal. The reciprocal of \(\displaystyle \frac{2}{3}\) is \(\displaystyle \frac{3}{2}\).

Therefore:

\(\displaystyle x*\frac{2}{3}*\frac{3}{2}=12*\frac{3}{2}\)

Since \(\displaystyle \frac{2}{3}*\frac{3}{2}=\frac{6}{6}=1\), we can ignore it.

\(\displaystyle x=12*\frac{3}{2}\)

\(\displaystyle x=\frac{12}{1}*\frac{3}{2}\)

\(\displaystyle x=\frac{36}{2}\)

\(\displaystyle x=18\)