Formula to calculate percentage

What is a percentage?

A percentage is a way to define a part, or fraction of a total.

When we talk about percentages, we should always ask ourselves the following: "the percentage of what?". Saying 50% without specifying 50% of what, makes no sense. However, if we say "the 50% 50\% of 80 80 " is 40 40 . In summary, the percentage represents what part of 100 100 is the number in question.

The percentage symbol is % \% :
when we want to express that a%a\%
We will write it as: a100a \over 100

To solve percentage problems, we will use the following formula

Percentage valueInitial amount=The percentage100 \frac{Percentage~value}{Initial~amount}=\frac{The~percentage}{100}

Percentage value: is the actual value that this percentage represents.

Initial amount: is the initial figure before being changed.
Percentage: is the percentage of change.

B - To solve percentage problems, we will use the following formula

You can use this formula for any percentage exercise, as long as you note the data correctly, and verify what has been asked.


Practice Percentage

Examples with solutions for Percentage

Exercise #1

Convert the following fraction into a percentage:

1520=? \frac{15}{20}=\text{?}

Video Solution

Step-by-Step Solution

A percentage is actually a form of a fraction, or more precisely, a fraction out of a hundred.

In other words, a fraction where the denominator is always 100.

Therefore, to convert a fraction to a percentage, we multiply it so that the denominator becomes 100.

20*5=100

15*5=75

So the fraction is 75/100, and the percentage is 75%.

Answer

75%

Exercise #2

How much is the 42 % of 15?

Video Solution

Step-by-Step Solution

To solve the exercise, first we will convert the percentage to its fractional form:

42%=42100 42\%=\frac{42}{100}

Now, we multiply the fractional form by 15

15×42100= 15\times\frac{42}{100}=

Let's break down the 15 for the multiplication exercise and also the 100 in the denominator for the multiplication exercise:

3×5×425×20 3\times5\times\frac{42}{5\times20}

Keep in mind that the five in the two exercises can be reduced to maintain the exercise:

3×4220=3×(2×21)2×10 3\times\frac{42}{20}=\frac{3\times(2\times21)}{2\times10}

Here we can also reduce the 2 in the numerator and the denominator:

3×2110=6310=6.3 \frac{3\times21}{10}=\frac{63}{10}=6.3

Answer

6.3

Exercise #3

The price of the movie ticket rose from 40 to 45 pesos By what percentage did the price increase?

Step-by-Step Solution

In order to answer the question we must first understand how much the ticket costs:

45-40=5

That is, the price of the ticket increased by 5$.

Now we need to determine what the percentage value of the 5 pesos increase is. In order to determine this we will divide the increase by the original price and multiply it by 100 to convert it into a percentage.

5/40 * 100

We start by converting the 100 into fraction form.

5/40 * 100/1

When there is a multiplication of fractions, we can multiply numerator by numerator and denominator by denominator.

5*100 / 40*1

500 / 40

Thus we simplify as follows:

50/4

Lastly we convert the fraction into its complete form.

50/4 = 12.5

Answer

12.5%

Exercise #4

A 20% discount is applied to a toy ordinarily priced at $40.

What is the new price after the discount?

Video Solution

Step-by-Step Solution

408=32 40-8=32 To find percentages, we must use two pieces of information we have: the total amount (40)andthediscount(2040) and the discount (20%).</p><p>This information can be placed in the following formula:</p><p><span class="katex">\( \frac{Price\times\text{Percentage}}{100} Which allows us to find the percentage of something.

We replace:

40×20100= 40\times\frac{20}{100}=
800100= \frac{800}{100}=

8 8

We discover that the value of the discount is 8.

But we are not finished yet!

We need to subtract the discount from the original amount to find the sale price:
\( 40-8=32

Answer

32

Exercise #5

What percentage is 20 out of 25?

Video Solution

Answer

80%

Exercise #6

What percentage is 32 out of 100?

Video Solution

Answer

32%

Exercise #7

What percentage is 5 out of 25?

Video Solution

Answer

20%

Exercise #8

What percentage is 40 out of 100?

Video Solution

Answer

40%

Exercise #9

What percentage is 9 out of 25?

Video Solution

Answer

36%

Exercise #10

What percentage is 2 out of 10?

Video Solution

Answer

20%

Exercise #11

What percentage is 2.6 out of 10?

Video Solution

Answer

26%

Exercise #12

What percentage is 8 out of 50?

Video Solution

Answer

16%

Exercise #13

What percentage is 4.4 out of 10?

Video Solution

Answer

44%

Exercise #14

What percentage is 2 out of 50?

Video Solution

Answer

4%

Exercise #15

What percentage is 24 out of 25?

Video Solution

Answer

96%