16 is what percent of 40?
solution
16 is 40% of 40.
explanation
Step 1: Translate the words into an equation.
16 | is | what percent | of | 40 |
16 | = | x | $ \cdot $ | 40 |
Step 2: Solve for $ x $.
$$ \begin{aligned} 16 &= x \cdot 40 \\[1.2 em] 40 \cdot x &= 16 \\[1.2 em] x &= \dfrac{ 16 }{ 40 } \\[1.2 em] x &= 0.4 \end{aligned} $$Step 3: Express $ x $ as a percentage.
$$ x = 0.4 = 0.4 ~~\cdot~~ 100 \% = 40 \% $$This calculator uses percentage formula to solves 5 types of percentage problems.
Example: What is 40% of 60?
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
Example: 16 is what percent of 40?
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.
$$ 0.375 = 0.375 \cdot 100 \% = 37.5 \% $$Example: Mark’s hourly salary is \$15. What is the percentage increase in the salary if it is raised to \$18?
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:
$$ \begin{aligned} \text{% increase} &= \dfrac{ 18 - 15 }{ 15 } \times 100 = \\[1.2em] &= \dfrac{ 3 }{ 15 } \times 100 = \\[1.2em] &= 0.2 \times 100 = \\[1.2em] & = 20 \% \end{aligned} $$Example: The workforce at a corporation decreased from 135 to 110 personnel. What is the percentage decrease in the number of employees?
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:
$$ \begin{aligned} \text{% increase} &= \dfrac{ 135 - 110 }{ 110 } \times 100 = \\[1.2em] &= \dfrac{ 25 }{ 110 } \times 100 = \\[1.2em] &= 0.227 \times 100 = \\[1.2em] & = 22.7 \% \end{aligned} $$Example: What percent of 80 is 25?
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.
$$ 0.3125 = 0.3125 \cdot 100 \% = 31.25 \% $$Please tell me how can I make this better.