Taking 32% of a number is the same as multiplying that number by 0.32. We therefore take the product:

\(\displaystyle 0.32 \cdot 2,000 = 640\)

Let's just pick a number at random, for example \(\displaystyle 100\). 

of this number is \(\displaystyle 25\), which is \(\displaystyle 100\) divided by \(\displaystyle 4\).

We can also work by simplifying the fractional form of . A percent can be written as the number divided by \(\displaystyle 100\).

\(\displaystyle =\frac{25}{100}\)

We can simplify this fraction: \(\displaystyle \frac{25}{100}=\frac{5}{20}=\frac{1}{4}\).

Either way, we get the same answer.

To find out what percent a part \(\displaystyle P\) is of a whole \(\displaystyle W\), evaluate the expression 

\(\displaystyle \frac{P}{W} \cdot 100 = \frac{3,300}{12,000} \cdot 100 = 27.5\) 

If \(\displaystyle 65\) is \(\displaystyle 12.5\%\) of a number, \(\displaystyle N\), then we can set up an equation. First, we convert \(\displaystyle 12.5\%\) to a decimal, \(\displaystyle 0.125\). Then, we can formulate the equation below.

\(\displaystyle 65 = 0.125N\)

Solve for \(\displaystyle N\) by dividing both sides of the equation by \(\displaystyle 0.125\).

\(\displaystyle \frac{0.125N}{0.125}=\frac{65}{0.125}\)

\(\displaystyle N = 520\)

First find the percentage amount for each choice by multiplying the number by the percentage amount

a. \(\displaystyle 90\ast .10=9\)

b. \(\displaystyle 160\ast .5=8\)

c. \(\displaystyle 50\ast .20=10\)

d. \(\displaystyle 40 \ast .30= 12\)

Then compare the amounts to find the largest.

The answer is (d) 12.

Set up the proportion statement and solve for \(\displaystyle N\) by cross-multiplying:

\(\displaystyle \frac{75}{N}= \frac{60}{100}\)

\(\displaystyle N \cdot 60 = 75 \cdot 100 = 7,500\)

\(\displaystyle N \cdot 60 \div 60 = 7,500\div 60\)

\(\displaystyle N = 125\)

Rewrite 120% as a decimal by writing 120 with a decimal point, then shifting it two spaces left:

\(\displaystyle 120.0\% = 1.20 = 1.2\)

Multiply this by 120:

\(\displaystyle 120 \times 1.2 = 144\)

Rewrite 225% as a decimal by writing 225 with a decimal point, then shifting it two spaces left:

\(\displaystyle 225.0\% = 2.25\)

Multiply this by 225:

\(\displaystyle 225 \times 2.25= 506.25\)

Rewrite 77% as a decimal by writing 77 with a decimal point, then shifting it two spaces left:

\(\displaystyle 77.0\% = 0.77\)

Multiply this by 77:

\(\displaystyle 77 \times 0.77 = 59.29\)

Set up a proportion, as follows:

\(\displaystyle \frac{N}{3,000} = \frac{\frac{1}{6}}{100}\)

Solve for \(\displaystyle N\) by cross-mutiplying:

\(\displaystyle 100 \cdot N = \frac{1}{6} \cdot 3,000\)

\(\displaystyle 100 \cdot N = \frac{1}{6} \cdot\frac{ 3,000}{1}\)

\(\displaystyle 100 \cdot N = 500\)

\(\displaystyle 100 \cdot N \div 100 = 500 \div 100\)

\(\displaystyle N = 5\)