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% 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.

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

Exercise #1

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 #2

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 #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

Answer

12.5%

Exercise #4

How much is 12% of 25?

Video Solution

Answer

3

Exercise #5

How much is 6% of 100?

Video Solution

Answer

6

Exercise #1

What is 20% of 50?

Video Solution

Answer

10

Exercise #2

What is 8% of 50?

Video Solution

Answer

4

Exercise #3

Convert the following fraction into a percentage:

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

Video Solution

Answer

75%

Exercise #4

What percentage is 2 out of 10?

Video Solution

Answer

20%

Exercise #5

What percentage is 5 out of 25?

Video Solution

Answer

20%

Exercise #1

What percentage is 12 out of 50?

Video Solution

Answer

24%

Exercise #2

What percentage is 2.6 out of 10?

Video Solution

Answer

26%

Exercise #3

What percentage is 9 out of 25?

Video Solution

Answer

36%

Exercise #4

What percentage is 8 out of 50?

Video Solution

Answer

16%

Exercise #5

What percentage is 20 out of 25?

Video Solution

Answer

80%