Introduction

We can find a percentage part of a number using the following formula: \textrm{part} = \textrm{percentage} \times \textrm{whole}

To illustrate, let's calculate 16 \% of 300.

Here, the whole is 300 and the percentage is 16 \% . So, the part is given by \textrm{part} = 16\% \times 300.

But how do we multiply a percentage by a number? We have two methods of doing this. Let's apply both and check that they give the same answer.

Method 1

First, we convert the percentage to a decimal: 16\% = 16 \div 100 = 0.16

Then, we apply our formula as follows:

\begin{align*} \textrm{part} &= \textrm{percentage} \times \textrm{whole} \\[5pt] &= 16\% \times 300 \\[5pt] &= 0.16 \times 300 \\[5pt] &= 48 \end{align*}

Therefore, 16\% of 300 is 48.

Method 2

First, we convert the percentage to a fraction: 16\% = \dfrac{16}{100}

Then, we apply our formula as follows:

\begin{align*} \textrm{part} &= \textrm{percentage}\times \textrm{whole} \\[5pt] &= 16\% \times 300 \\[5pt] &= \dfrac{16}{100} \times 300 \\[5pt] &= 16 \times \dfrac{300}{100} \\[5pt] &= 16 \times 3 \\[5pt] &= 48 \end{align*}

Therefore, 16 \% of 300 is 48.

FLAG
Example: Finding Part of a Number Given a Whole and a Percentage

What is 4 \% of 35?

EXPLANATION

To solve this problem, we can use the following formula:

\textrm{part}= \textrm{percentage}\times \textrm{whole}

In our case, the whole is 35 , and the percentage is 4 \%.

Method 1

First, we convert the percentage to a decimal:

4 \% = 4 \div 100 = 0.04

Then, we apply our formula as follows:

\begin{align} \textrm{part}&= \textrm{percentage}\times \textrm{whole} \\[5pt] & = 4 \% \times 35 \\[5pt] & = 0.04 \times 35 \\[5pt] & = 1.4 \end{align}

Therefore, 4 \% of 35 is 1.4.

Method 2

First, we convert the percentage to a fraction:

4 \% = \dfrac{4}{100}

Then, we apply our formula as follows:

\begin{align} \textrm{part}&= \textrm{percentage}\times \textrm{whole} \\[5pt] & = 4 \% \times 35 \\[5pt] & = \dfrac{4}{100} \times 35 \\[5pt] & = \dfrac{140}{100}\\[5pt] & = 1.4 \end{align}

Therefore, 4 \% of 35 is 1.4.

FLAG
Practice: Finding Part of a Number Given a Whole and a Percentage

What is $20\%$ of $40?$

a
 $4$
b
 $6$
c
 $16$
d
 $8$
e
 $12$
Practice: Finding Part of a Number Given a Whole and a Percentage

What is $3\%$ of $60?$

a
 $0.6$
b
 $1.2$
c
 $1.5$
d
 $1.8$
e
 $0.9$
Example: Finding Part of a Number Given a Whole and a Percentage Greater Than 100%

What is 140 \% of 30?

EXPLANATION

To solve this problem, we can use the following formula:

\textrm{part}= \textrm{percentage}\times \textrm{whole}

In our case, the whole is 30 , and the percentage is 140\%.

Method 1

First, we convert the percentage to a decimal:

140 \% = 140 \div 100 = 1.4

Then, we apply our formula as follows:

\begin{align} \textrm{part}&= \textrm{percentage}\times \textrm{whole} \\[5pt] & = 140 \% \times 30 \\[5pt] & = 1.4 \times 30 \\[5pt] & = 42 \end{align}

Therefore, 140 \% of 30 is 42.

Method 2

First, we convert the percentage to a fraction:

140 \% = \dfrac{140}{100} = \dfrac{140 \div 20}{100\div 20} = \dfrac{7}{5}

Then, we apply our formula as follows:

\begin{align} \textrm{part}&= \textrm{percentage}\times \textrm{whole} \\[5pt] & = 140 \% \times 30 \\[5pt] & = \dfrac{7}{5} \times 30 \\[5pt] & = 7 \times \dfrac{30}{5}\\[5pt] & = 7 \times 6\\[5pt] & = 42 \end{align}

Therefore, 140 \% of 30 is 42.

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Practice: Finding Part of a Number Given a Whole and a Percentage Greater Than 100%

What is $120 \%$ of $25?$

a
 $35$
b
 $24$
c
 $27$
d
 $30$
e
 $32$
Practice: Finding Part of a Number Given a Whole and a Percentage Greater Than 100%

What is $110\%$ of $20?$

a
 $24$
b
 $22$
c
 $21$
d
 $25$
e
 $23$
Example: Finding Part of a Number Given a Whole and a Decimal Percentage

What is 3.6 \% of 25?

EXPLANATION

To solve this problem, we can use the following formula:

\textrm{part}= \textrm{percentage}\times \textrm{whole}

In our case, the whole is 25 , and the percentage is 3.6 \%.

Method 1

First, we convert the percentage to a decimal:

3.6 \% = 3.6 \div 100 = 0.036

Then, we apply our formula as follows:

\begin{align} \textrm{part}&= \textrm{percentage}\times \textrm{whole} \\[5pt] &= 3.6 \% \times 25 \\[5pt] &= 0.036 \times 25 \\[5pt] &=0.9 \end{align}

Therefore, 3.6 \% of 25 is 0.9.

Method 2

First, we convert the percentage to a fraction:

3.6 \% = \dfrac{3.6}{100} = \dfrac{3.6 \times 10}{100 \times 10} = \dfrac{36}{1,000}

Then, we apply our formula as follows:

\begin{align} \textrm{part}&= \textrm{percentage}\times \textrm{whole} \\[5pt] &= 3.6 \% \times 25 \\[5pt] &= \dfrac{36}{1,000} \times 25 \\[5pt] &=\dfrac{900}{1,000}\\[5pt] &=0.9 \end{align}

Therefore, 3.6 \% of 25 is 0.9.

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Practice: Finding Part of a Number Given a Whole and a Decimal Percentage

What is $3.2 \%$ of $125?$

a
 $5.1$
b
 $4.4$
c
 $4.0$
d
 $3.5$
e
 $3.8$
Practice: Finding Part of a Number Given a Whole and a Decimal Percentage

What is $0.3 \%$ of $500?$

a
 $1.8$
b
 $1.4$
c
 $1.6$
d
 $1.2$
e
 $1.5$
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