Percentage - Examples, Exercises and Solutions

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 $50\%$ of $80$" is $40$. In summary, the percentage represents what part of $100$ is the number in question.

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

To solve percentage problems, we will use the following formula

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

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.

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

Exercise #1

How much is the 42 % of 15?

Step-by-Step Solution

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

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

Now, we multiply the fractional form by 15

$15\times\frac{42}{100}=$

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

$3\times5\times\frac{42}{5\times20}$

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

$3\times\frac{42}{20}=\frac{3\times(2\times21)}{2\times10}$

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

$\frac{3\times21}{10}=\frac{63}{10}=6.3$

6.3

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 $40-8=32$To find percentages, we must use two pieces of information we have: the total amount ($40) and the discount (20%). This information can be placed in the following formula: \( \frac{Price\times\text{Percentage}}{100}$ Which allows us to find the percentage of something. We replace: $40\times\frac{20}{100}=$ $\frac{800}{100}=$ $8$ 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 #3 The price of to movie ticket htos risen from 40 to 45 pesos By whtot percenttoge did the price incretose? Step-by-Step Solution To answer the question, first we have to understand how much the ticket costs: 45-40=5 That is, the price of the ticket went up by 5$.

Now we would like to know what is the percentage value of 5 and, for that, we will divide the increase by the original price and multiply it by 100 to convert it into a percentage.

5/40 * 100

First we can start by converting the 100 into fraction form.

5/40 * 100/1

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

5*100 / 40*1

500 / 40

We simplify:

50/4

And now we will move to the complete form.

50/4 = 12.5

12.5%

Exercise #4

How much is 12% of 25?

3

Exercise #5

How much is 6% of 100?

6

Exercise #1

What is 20% of 50?

10

Exercise #2

What is 8% of 50?

4

Exercise #3

Convert the following fraction into a percentage:

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

75%

Exercise #4

What percentage is 2 out of 10?

20%

Exercise #5

What percentage is 5 out of 25?

20%

Exercise #1

What percentage is 12 out of 50?

24%

Exercise #2

What percentage is 2.6 out of 10?

26%

Exercise #3

What percentage is 9 out of 25?

36%

Exercise #4

What percentage is 8 out of 50?