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Percentage calculator
This calculator is a free online math tool that solves eight types of percentage problems. Just input the values into the sentence that best describes the problem involving percentages, and the calculator will generate a step-by-step solution.
How to solve percentage problems?
This calculator solves eight different types of percenatge problems. We will use some examples to show each type.
Type 1: What is x % of y?
Example:What is 40% of 60?
Solution:
Step1: Change the 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 for $ x $
$$ \begin{aligned} 15 &= x \cdot 40 \\ 40 \cdot x &= 15 \\ x &= \frac{15}{40} \\ x &= 0.375 \\ \end{aligned} $$Step3: Multiply x by 100% to convert the result to a percentage.
$$ 0.375 = 0.375 \cdot 100 \% = 37.5 \% $$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 apply the percentage increase formula:
$$ \text{% increase} = \dfrac{ \text{final amount} - \text{ initial amount} }{ \text{ initial amount} } \times 100 $$After putting the initial amount to 15 and the final amount to 18, we get:
$$ \begin{aligned} \text{% increase} &= \dfrac{ 18 - 15 }{ 15 } \times 100 = \\[1.2em] &= \dfrac{ 3 }{ 15 } \times 100 = \\[1.2em] &= 0.2 \times 100 = \\[1.2em] & = 20 \% \end{aligned} $$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 the initial amount to 135 and final amount to 110 we get:
$$ \begin{aligned} \text{% increase} &= \dfrac{ 135 - 110 }{ 135 } \times 100 = \\[1.2em] &= \dfrac{ 25 }{ 135 } \times 100 = \\[1.2em] &= 0.185 \times 100 = \\[1.2em] & = 18.5 \% \end{aligned} $$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 for $ 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%.
$$ 0.3125 = 0.3125 \cdot 100 \% = 31.25 \% $$