# Percents

In this post we will learn concept of Percent or Percentage.
We will take the help of images for conceptual understanding.

After the concept, we will solve some practice exercise at the end of the chapter.

## What is Percent?

The word percent means “per 100”

It basically tells you the amount of unit present in 100 unit.

The symbol used to express percent is %.
Hence, if 5% is written, it means 5 percent.

Lets us understand the theory behind it using images.

### Percent Explanation using Images

Different set of image examples are given below.
Study the image and the explanation to learn the concept of Percent.

Example 01

The below image is of square with 100 boxes.
Total Box = 100
Box with Green Color = 3

Out of 100 box there are 3 boxes of green color.

Hence there are 3 green box per 100 box.
So, Percentage of Green Box = 3%

Example 02

Consider similar example where 12 box are colored in Green

Green Box = 12
Colored Box = 100

So out of 100 boxes, there are 12 green box

Hence the percentage of green box = 12%

Example 03

Below image contain all the green boxes.

Total Boxes = 100
Green Box = 100

There are 100 green boxes per 100 box
Hence the percentage is 100%

In Percentage, 100% means all/full

Example 04

The below box contain 50 green box

Total Box = 100
Green Box = 50

So for 100 total box, there are 50 Green boxes

Hence percentage for Green box = 50%

In the below image you can see that 50% covers half of the box.

### Percentage using Observation

Sometimes there is no need to do any calculation.
You can tell the percentage of the figure just by observing the given image.

### Manual Calculation of Percent

In this section, a percentage number is provided to you.
We will find the number of colored boxes using percentage information given to us.

Given below is the square grid with total of 80 boxes inside.
We have to paint the small boxes blue as per the required condition.

How much box do we have to paint to make 50% blue?

We already know that for 50% we have to make half of the image blue.

100% Box = 80

50% green box
\Longrightarrow \ \frac{50}{100} \ \times 80\\\ \\ \Longrightarrow \ 40

Hence for 50%, we need to paint 40 boxes

How much box we have to paint for 30% blue?

100% Box = 80

30% Blue Calculation
\Longrightarrow \ \frac{30}{100} \ \times 80\\\ \\ \Longrightarrow \ 24 \\\ \\

Hence 24 boxes need to be painted for 30%

### Percentage as Fraction

While using percentage in basic calculation we should know how to represent percentage in the form of fraction. This will help us in algebra related calculation.

You can represent percentage into fraction by inserting denominator 100.

1% can be represented as \frac{1}{100}

7% ⟹ \frac{7}{100}

25% ⟹ \frac{25}{100}

50% ⟹ \frac{50}{100}

100% ⟹ \frac{100}{100}

### Calculation of Percentage

you can calculate the percent of any number by using formula

Result = \frac{Percentage}{100} \times \ Total Value

Let us understand the formula with the help of examples:

Example 01
Find 25% of number 100

Here,
Percentage given = 25%
Total Value = 100

Result\ =\ \frac{25}{100} \times \ 100\\\ \\ Result\ =\ 25

Example 02
Find 40% of number 70

Percentage given = 40
Total Value = 70

Result\ =\ \frac{40}{100} \times \ 70\\\ \\ Result\ =\ 28

Example 03
In a class there are 60 kids. Only 30% kids are present today. Find the number of kids present in class.

Percentage given = 30%
Total Value = 60

Result\ =\ \frac{30}{100} \times \ 60\\\ \\ Result\ =\ 18

Hence total of 18 kids are present in school today

Example 04
Paul scored 70% marks on a total of 180. Calculate the actual marks scored by Paul.

Percentage = 70%
Total Value = 180

Result\ =\ \frac{70}{100} \times \ 180\\\ \\ Result\ =\ 126

Hence 126 is the total marks

## Percent Problems – Grade 5

Given below are the set of problems related to Percentage theory discussed above.
Request to all students to take pen and pencil out and solve each of the given question.

(01) 5% of 20

(a) 4
(b) 2
(c) 1
(d) 6

Result\ =\ \frac{5}{100} \times \ 20\\\ \\ Result\ =\ 1 \\\ \\

Option (c) is the right answer

(02) 10% of 240

(a) 24
(b) 20
(c) 18
(d) 28

Result\ =\ \frac{10}{100} \times \ 240\\\ \\ Result\ =\ 24 \\\ \\

Option (a) is the right answer

(03) 15% of 360

(a) 70
(b) 52
(c) 74
(d) 54

Result\ =\ \frac{15}{100} \times \ 360\\\ \\ Result\ =\ 54 \\\ \\

Option (d) is the right answer

(04) 20% of 200

(a) 60
(b) 40
(c) 50
(d) 70

Result\ =\ \frac{20}{100} \times \ 200\\\ \\ Result\ =\ 40 \\\ \\

Option (b) is the right answer

(05) 25% of 150

(a) 35
(b) 40
(c) 32.5
(d) 37.5

Result\ =\ \frac{25}{100} \times \ 150\\\ \\ Result\ =\ 37.5 \\\ \\

Option (d) is the right answer

(06) 9% of 18

(a) 1.62
(b) 1.5
(c) 1.73
(d) 2.5

Result\ =\ \frac{9}{100} \times \ 18\\\ \\ Result\ =\ 1.62 \\\ \\

Option (a) is the right answer

(07) 30% of 50

(a) 12
(b) 15
(c) 20
(d) 18

Result\ =\ \frac{30}{100} \times \ 50\\\ \\ Result\ =\ 15 \\\ \\

Option (b) is the right answer

(08) 22% of 500

(a) 120
(b) 80
(c) 110
(d) 100

Result\ =\ \frac{22}{100} \times \ 500\\\ \\ Result\ =\ 110 \\\ \\

Option (c) is the right answer

(09) 90% of 1000

(a) 90
(b) 700
(c) 900
(d) 800

Result\ =\ \frac{90}{100} \times \ 1000\\\ \\ Result\ =\ 900 \\\ \\

Option (c) is the right answer

(10) 6% of 36

(a) 2.16
(b) 3.14
(c) 6.63
(d) 4.5