Percentage calculator with all steps (2024)

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Find 45% of 120.

What is 45% of 60 %

150 is what percent of 400?

What is the percentage increase from to 50 to 75?

The student received a 60% on a maths exam that included 20 problems.How many problems did the student properly answer on this test?

The whale population numbers 140 pairs. If the number of pairs increases by 8%, how many pairs will there be altogether?

The workforce at a corporation decreased from 40 to 29 personnel. What is the percentage decrease in the number of employees?

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

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:

$$\text{% increase} = \dfrac{ \text{final amount} - \text{ initial amount} }{ \text{ initial amount} } \times100$$

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 thepercentage decrease in the number of employees?

Solution:

To solve this problem we use percentage decrease formula:

$$\text{% decrease} = \dfrac{ \text{initial amount} - \text{ final amount} }{ \text{ initial amount} } \times100$$

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

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%.

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