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One number as a percentage of another

 

One number as a percentage of another 

When you express one number as a percentage of another, you're essentially comparing the first number to the second number in terms of proportion or relative size. This is commonly used to understand the relationship between two quantities.

The formula to calculate one number as a percentage of another is:

$\text{Percentage}=\left(\frac{\text{First Number}}{\text{Second Number}}\right)\times 100\mathrm{\%}$Percentage=(Second NumberFirst Number​)×100%

For example, let's say you have 25 apples and 100 oranges. To express the number of apples as a percentage of the number of oranges, you would use the formula:

$\text{Percentage of apples}=\left(\frac{25}{100}\right)\times 100\mathrm{\%}$Percentage of apples=(10025​)×100%

$\text{Percentage of apples}=0.25\times 100\mathrm{\%}$Percentage of apples=0.25×100%

$\text{Percentage of apples}=25\mathrm{\%}$Percentage of apples=25%

So, 25 apples represent 25% of the total number of oranges.

This calculation can be used in various contexts, such as comparing the number of students who passed an exam to the total number of students, expressing a portion of a budget relative to the total budget, or determining the proportion of a population that belongs to a certain demographic group.

 

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Reverse Percentage

Reverse percentage, also known as backwards percentage or inverse percentage, refers to the process of finding the original value when only the final value and the percentage change are known. It involves determining what the original amount was before a certain percentage increase or decrease occurred.

The formula for reverse percentage can be expressed as:

$\text{Original Value}=\frac{\text{Final Value}}{1+(\text{Percentage Change}\mathrm{/}100)}$

or

$\text{Original Value}=\frac{\text{Final Value}}{1-(\text{Percentage Change}\mathrm{/}100)}$

depending on whether it's a percentage increase or decrease, respectively.

For example, if a product's price increased by 20% and the final price is $120, you can use reverse percentage to find the original price:

$\text{Original Price}=\frac{120}{1+(20\mathrm{/}100)}$

$\text{Original Price}=\frac{120}{1.2}$

$\text{Original Price}=100$

So, the original price of the product was $100 before the 20% increase.

Reverse percentage calculations are useful in various real-life scenarios, such as determining the original price of a discounted item, calculating the original quantity of a substance before dilution or concentration, or figuring out the initial value of an investment before a certain percentage gain or loss.

 

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