$\displaystyle \small \small 21\tfrac{1}{3}$ %   $\displaystyle \small = \small \small \frac{21\frac{1}{3}}{100} = 21\frac{1}{3} \div 100 = \frac{64}{3} \div \frac{100}{1} = \frac{64}{3} \cdot \frac{1}{100}$

Cross-cancel by dividing 64 and 100 by 4:

$\displaystyle \small \small \frac{64}{3} \cdot \frac{1}{100} = \frac{16}{3} \cdot \frac{1}{25} = \frac{16}{75}$, 

which is the fraction we want.

$\displaystyle \frac{1}{7} \%$ of $\displaystyle 154,000$ can be calculated as follows.

First, we need to convert $\displaystyle \frac{1}{7} \%$ into a fraction that we can use in calculations. The percentage symbol tells us that the value is divided by $\displaystyle 100$.

$\displaystyle \frac{1}{7}\% =\frac{\frac{1}{7}}{100}$

Now we can multiply our given value by this fraction to find our answer.

$\displaystyle \frac{\left (\frac{1}{7}) \right }{100}*154,000=\frac{\left (\frac{1}{7})*154,000 \right }{100}= \frac{22,000}{100}=220$

Set up a proportion statement:

$\displaystyle \frac{\frac{1}{2}}{100} = \frac{N}{\frac{1}{3}}$

Cross-multiply and solve for $\displaystyle N$:

$\displaystyle N \cdot 100 = \frac{1}{2} \cdot \frac{1}{3}$

$\displaystyle N \cdot 100 = \frac{1}{6}$

$\displaystyle N \cdot 100 \cdot \frac{1}{100} = \frac{1}{6} \cdot \frac{1}{100}$

$\displaystyle N = \frac{1}{600}$

Set up a proportion statement:

$\displaystyle \frac{P}{100} = \frac{\frac{1}{5}}{1 \frac{2}{5}}$

Simplify the right side and solve for $\displaystyle P$:

$\displaystyle \frac{P}{100} = \frac{1}{5} \div 1 \frac{2}{5} = \frac{1}{5} \div \frac{7}{5} = \frac{1}{5} \cdot \frac{5}{7} = \frac{1}{7}$

$\displaystyle \frac{P}{100} \cdot 100 = \frac{1}{7}\cdot 100$

$\displaystyle P= \frac{100}{7} = 14 \frac{2}{7}$

Let $\displaystyle P$ be the percent. Then

$\displaystyle P = \frac{ 0.0003}{0.6} \cdot100 = 0.05$

Set up the proportion statement:

$\displaystyle \frac{N}{1\frac{1}{4}} = \frac{1\frac{1}{4}}{100}$

Cross-multply and solve for $\displaystyle N$:

$\displaystyle 100 N=1 {\frac{1}{4}} \cdot 1{\frac{1}{4}} = {\frac{5}{4}} \cdot {\frac{5}{4}}$

$\displaystyle 100 N= {\frac{25}{16}}$

$\displaystyle \frac{1}{100} \cdot 100 N=\frac{1}{100} \cdot {\frac{25}{16}}$

$\displaystyle N =\frac{1}{100} \cdot {\frac{25}{16}}= \frac{1}{4} \cdot {\frac{1}{16}}= \frac{1}{64}$

Set up the proportion statement:

$\displaystyle \frac{N}{\frac{1}{4}} = \frac{\frac{1}{4}}{100}$

Cross-multply and solve for $\displaystyle N$:

$\displaystyle 100 N= {\frac{1}{4}} \cdot {\frac{1}{4}}$

$\displaystyle 100 N= {\frac{1}{16}}$

$\displaystyle \frac{1}{100} \cdot 100 N=\frac{1}{100} \cdot {\frac{1}{16}}$

$\displaystyle N = \frac{1}{1,600}$

Set up a proportion:

$\displaystyle \frac{\frac{2}{3}}{100} = \frac{N}{\frac{2}{5}}$

Cross-multiply and solve for $\displaystyle N$:

$\displaystyle N \cdot 100 = \frac{2}{3} \cdot \frac{2}{5}$

$\displaystyle N \cdot 100 = \frac{4}{15}$

$\displaystyle N \cdot 100 \cdot \frac{1}{100} = \frac{4}{15} \cdot \frac{1}{100}$

$\displaystyle N = \frac{4}{1,500} = \frac{1}{375}$

There are a few ways we can approach this problem. We know that $\displaystyle \small \frac{3}{5}\%$ is $\displaystyle \small \frac{\frac{3}{5}}{100 }$, or $\displaystyle \small \frac{3}{5}*\frac{1}{100}$.

We also know that for percentages, "of" means multiply, so we can set up a multiplication problem: 

$\displaystyle \small \small \frac{3}{5}*\frac{1}{100}*450$

Simplifying gives

$\displaystyle \small \small \frac{1350}{500}=2.7$.

Remember that the word "of" means multiply. One way to solve this is to first divide the percentage by 100.

$\displaystyle \frac{\frac{1}{2}}{100}$

This is the division of two fractions and can be done by multiplying the first fraction by the reciprocal of the second fraction. Remember to treat $\displaystyle 100$ as the fraction $\displaystyle \frac{100}{1}$

The multiplication should look like this

$\displaystyle \frac{1}{2}\cdot \frac{1}{100}$

Now multiply across the numerator and denominator

$\displaystyle \frac{1}{200}$

Now that the fractional percentage has been converted to a regular fraction we can multiply this by the $\displaystyle 300,000$ to get the answer

$\displaystyle \frac{1}{200}\cdot \frac{300000}{1}$

$\displaystyle \frac{300000}{200}$

$\displaystyle 1500$