GENERATE WORK

GENERATE WORK

**Input Data : **

From Value = 6000

To Value = 7200

**Objective : **

Find what percent increase is from 6000 to 7200?

**Formula **

`\text{Percent increase} = \frac{\text{To Value - From Value}}{\text{From Value}} \times 100`

Percent increase` = \frac{7200 - 6000}{6000} \times 100`

` = \frac{1200}{6000} \times 100`

` = \frac{120000}{6000}`

Percent increase `= 20%`

** Percentage increase calculator** uses two values, original $X$ and final $Y$ such that $X\lt Y$ and $X\ne0$, and calculate the percent of increase from the original to final.
In other words, it determines the change of quantity to a larger amount in terms of percent. It is an online a mathematical tool requires two real numbers, and determines the amount of a profit as a percentage of the original number.

It is necessary to follow the next steps:

- Enter the original and final values in the box. The original value must be less than the final. These values must be real numbers, whereas the original value must be nonzero;
- Press the
**"GENERATE WORK"**button to make the computation; - Percentage increase calculator will give the percent of increase from the first amount to the second one.

If the original amount is less than the final amount, then the percent of increase is determined by the following formula

$$\rm{percent\;of\;increase}=\Big(\frac{\rm{final\;amount}-\rm{original\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%,\quad\rm{original\;amount}\ne0$$

A percent of change is increased or decreased the percent an amount in relation to the original amount. The formula for the percent change is

$$\rm{percent\;change}=\Big(\frac{\rm{final\;amount-original\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%,\quad\rm{original\;amount}\ne0$$

or

$$\frac{\rm{percent\;change}}{100}=\Big(\frac{\rm{actual\;change}}{|\rm{original\;amount}|}\Big)\times 100\%,\quad\rm{original\;amount}\ne0$$

When an amount increases, i.e the percent change is positive, then the percent of change is a percent of increase. When an amount increases, i.e the percent change is negative, then the percent of change is a percent of increase.

For example, in $1968$, the price per liter of diesel was $\$1.17.$ In $2018$, the price per liter was $\$1.37.$ So, this is a change in price of $\$0.2$ per liter. The relation between the original and new price can be expressed in terms of ratio:

$$\begin{align} {\rm{percent\;change}}&=\Big(\frac{\rm{changing\;in\;price}}{\rm{original\;price}}\Big)\times 100\%\\
&=\Big(\frac{\rm{\;price\;in\;2018-price\;in\;1968}}{\rm{price\;in\;1968}}\Big)\times 100\%\\
&=\Big(\frac{1.37-1.17}{1.17}\Big)\times 100\%\\
&=\frac{0.2}{1.17}\times 100\%\\
&\approx 17.09\%\end{align} $$

The percent of change is $17.09\%$. Since the percent of change is positive, the percent of change is a
percent of increase, so compared to the original price, the new price increased by about $17.09\%$.Since the original amount is less than the final amount, the percent of increase is fully determined by the formula

$$\rm{percent\;of\;increase}=\Big(\frac{final\;amount-\rm{original\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%,\quad\rm{original\;amount}\ne0$$

If the percent of increase and the original amount are known, then the final amount can be found by using the following formula:

$$\rm{final\;amount}={\rm{percent\;of\;increase}}\times|{\rm{original\;amount}}|+{\rm{original\;amount}}$$

If the original amount is less than the final amount, then the percent of change increased. If the percent of change increased, then the percent of change is a percent of increase and vise versa.
The percent of increase is the difference between a final and original amounts divided by the absolute value of the original amount and multiplied by $100\%$.

The percentage increase work with steps shows the complete step-by-step calculation for finding the percent of increase from one amount to another with the original (initial) value of $80$ and the final value of $120$. For any other combinations of the original and final value, just supply values and click on the "GENERATE WORK" button. The grade school students may use this percentage increase calculator to generate the work, calculate how much the price increase, verify the results or do their homework problems efficiently.

In the real life, usually prices go up, our weight goes up, population grows etc. For instance, the price increase can be measured as a percentage of the original price. Interpreting the amount of change as a percent of increase is useful to compare two parameters. The percent of increase is useful in transactions such as sales, costs, expenses and profits.

**Practice Problem 1:**

Michael had been earning salary of $\$1600$ per month. He get a increase to $\$2000$ per month. Find the percent of increase.

**Practice Problem 2:**

Find the percent of increase from $100$ to $1300$.

The ercentage increase calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students (K-12 education) to learn how to find percent of increase from one number to another. This concept is very useful in real-life, for instance, to determine the price of the product when it goes up.