Percentage calculator

Type 1: What is x % of y?

Example: What is 40% of 60?

Solution:

Step1: Change word of to multiplication sign.

40% of 60 = 40% * 60

Step2: Change 40% to decimal number by dividing 40% by 100 [ 40% = 40/100 = 0.4 ]

40% * 60 = 0.4 * 60 = 24

Type 2: x is what percent of y?

Example: 16 is what percent of 40?

Solution:

Step1: Translate the words into an equation

16	is	what percent	of	40
16	=	x	$ \cdot $	40

Step2: Solve the $ x $

$$ \begin{aligned} 15 &= x \cdot 40 \\ 40 \cdot x &= 15 \\ x &= \frac{15}{40} \\ x &= 0.375 \\ \end{aligned} $$

Step3: Express $ x $ as a percentage (fraction of 100) by multiplying the result by 100.

$$ 0.375 = 0.375 \cdot 100 \% = 37.5 \% $$

Type 3: Percentage increase

Example: Mark’s hourly salary is \$15. What is the percentage increase in the salary if it is raised to \$18?

Solution:

To solve this problem we use percentage increase formula:

$$ \text{% increase} = \dfrac{ \text{final amount} - \text{ initial amount} }{ \text{ initial amount} } \times 100 $$

After putting initial amount = 15 and final amount = 18 we have:

$$ \begin{aligned} \text{% increase} &= \dfrac{ 18 - 15 }{ 15 } \times 100 = \\[1.2em] &= \dfrac{ 3 }{ 15 } \times 100 = \\[1.2em] &= 0.2 \times 100 = \\[1.2em] & = 20 \% \end{aligned} $$

Type 4: Percentage decrease

Example: The workforce at a corporation decreased from 135 to 110 personnel. What is the percentage decrease in the number of employees?

Solution:

To solve this problem we use percentage decrease formula:

$$ \text{% decrease} = \dfrac{ \text{initial amount} - \text{ final amount} }{ \text{ initial amount} } \times 100 $$

After putting initial amount = 135 and final amount = 110 we have:

$$ \begin{aligned} \text{% increase} &= \dfrac{ 135 - 110 }{ 110 } \times 100 = \\[1.2em] &= \dfrac{ 25 }{ 110 } \times 100 = \\[1.2em] &= 0.227 \times 100 = \\[1.2em] & = 22.7 \% \end{aligned} $$

Type 5: What percent of X is Y?

Example: What percent of 80 is 25?

Solution:

Step1: Translate the words into an equation

What percent	of	80	is	25
x	$\cdot$	80	=	25

Step2: Solve the $ x $

$$ \begin{aligned} x \cdot 80 &= 25 \\ x &= \frac{25}{80} \\ x &= 0.3125 \\ \end{aligned} $$

Step3: Express $ x $ as a percentage by multiplying the result by 100.

$$ 0.3125 = 0.3125 \cdot 100 \% = 31.25 \% $$