**Percent** is a way of expressing a number as a fraction of 100 (which means “out of 100”), that is, it is an amount that corresponds proportionally to a part of one hundred. In various activities of daily life the comparison between numbers is applied . To facilitate comparison, many numerical data are related in practice to the number 100.

Related to the calculation of percent, three different cases can be presented:

1. Find what number is the percent of another.

2. Find what Percent is a number of another

3. Find a number, given another number that is a Percent of it.

## Summary

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- 1 Significance of Percent
- 2 Percent Calculation
- 1 Exercises solved

- 3 How much percent is one number of another
- 4 How to calculate How much percent is one number of another
- 1 Solved exercises

- 5 How to Find a Known Number Percent of It
- 1 Solved exercises

- 6 External links
- 7 Sources

## Percent Significance

The information expressed in “Percent” is commonly observed, for which the% symbol is used, which is written immediately after the number to which it refers, without leaving a space. This means So many per cent, that is, the elements that are taken from each set of 100. It is important to know how to interpret the information that is shown in So many percent and that means So many of each 100, that is, the elements that are taken gives each set of 100.

For example (1), It says: “50% of 300 is 150” or “150 is 50% of 300”

This is interpreted as follows:

Fig. 1TxC.JPG

300 is made up of 3 groups of 100

50% means that for each percent 50 are taken

Therefore, to find 50% of 300, 3 times 50 are taken, that is: 3 * 50 = 150 (which is the same as 50+ 50 + 50 = 150)

This procedure is very uncomfortable when it comes to very large numbers, so it is convenient to simplify it, for this it is recommended to use another method. For example (2), when you want to find 6% of 2400. This means that of each set of 100 that 2400 owns, you must take 6, that is, the part of the set that is taken is 6/100, that is 0 , 06; all this means that finding 6% of a number is equivalent to finding 6/100 of said number (in this case 2400), that is, 6/1 00 * 24 00 = 6 * 24 = 144 or also 0.06 * 2400 = 144

This procedure works without difficulty for when the number or percent is any fractional.

Example (3) What is 19.2% of 70?

In this case we proceed as in the previous example, that is, 19.2 are taken from every 100, which means that the part of 100 that represents 19.2% can be expressed as 19.2 / 100; this is to find 19.2%, what remains as follows: 19.2 / 10 0 * 7 0 = 1.92 * 7 = 13.44 or also 0.06 * 2400 = 144. This procedure works without difficulty when the number or percent is any fractional.

Another way is: 0.192 * 70 = 13.44. Hence 19.2% of 70 is 13.44.

## Percent calculation

To calculate the Percent of a number multiply the number by the Percent (expressed as a division of divisor 100 or in decimal notation by running the comma two places to the left)

For example (4) To calculate 3% 45 is multiplied 45 by 3/100 (which is the same as 3/100 * 45) or 45 is multiplied by 0.03, which is mathematically expressed as: 45 ^{9} * 3/100 ^{20} = 9 * 3/20 = 27/20 = 1.35 or 45 * 0.03 = 1.35. From both routes it is obtained that 3% of 45 is 1.35; which is the same as: 1.35 is 3% of 45.

### Exercises solved

- Calculate 12% of 300

Answer: 300^{3}* 2/100= 3 * 12 = 36 or 300 * 0.12 = 36

12% of 300 is 36. - Calculate 25 5%

A: 25^{1}* 5/ 100^{4}= 5/4 = 1.25 or 25 * 0.05 = 1.25

The 5% is 1.25 25 - Calculate 69% of 21

Answer: 21 * 69/100 = 21 * 0.69 = 14.49 69% of 21 is 14.49 - Calculate 53% of 187

Answer: 187 * 0.53 = 99.11

53% of 187 is 99.11 - Calculate 4.2% of 26m

Answer: 26m * 0.042 = 1.092m

4.2% of 26m is 1.092m - Calculate 6% of $ 713

Answer: $ 713 * 0.06 = 42.78

6% of $ 713 is $ 42.78 - Calculate 2.34% of 505g

Answer: 505g * 0.0234 = 11.817g

2.34% of 505g is 11.817g - In a school there are 620 students, 55% of them are boys. How many boys are there?

To solve this problem what is needed is to calculate 55% of 620

Answer: 620 * 0.55 = 341

There are 341 boys at school. - A worker in a garment workshop planned to produce 156 shirts in the month, but only 75% of them were made. How many shirts did you make?

This problem is solved by calculating 75% of 156

Answer: 156 * 0.75 = 117

The worker made 117 shirts.

## How much percent is one number of another

Frequently there is a need to know how much percent is a number of another, that is, what part is a number of another (so far we have only tried to calculate the percent of a number). For example: what percent is 25 out of 32. This has practical application in various situations such as the following: The number of females enrolled in three schools behaves as shown in the table. Example (5)

Center | Enrollment | Number of females |

Center A | 400 | 180 |

Center B | 75 | 30 |

Center C | 63 | 16 |

Which of the three centers has more females with respect to the total enrollment?

Here it is necessary to compare. One way to do this is to analyze what part of the license plate the females represent.

This implies that three fractions are formed:

Center A: Center B: Center C:

180/400 30/75 30/75

There are now three fractions to compare, which can be done by multiplying crosswise and comparing the results (a path studied in the contents corresponding to working with fractions)

180 * 75 = 13 500 400 * 30 = 12,000, hence : 180/400> 30/75 Then: 180 * 63 = 11 340 400 * 16 = 6 400, hence 180/400> 16/63.

From this it is concluded that Center A has more females registered.

Notwithstanding the above, in practice it is widely used to solve situations of this type by comparing the fractions as Percent. For this, the ideal is to divide in each case the number of females by the enrollment and express the quotient as a percent.

Center A 180/400 = 9/20 = 0.45 45%

Center B 30/70 = 6/25 = 0.4 40%

Center C 16/63 = 0.25396825 = 0.25 (applying rounding rules) 25.4%

## How To Calculate How Much Percent Is One Number From Another

To calculate how much percent is one number of another, divide the first by the second and the quotient (result of the division) is expressed as a percent (by moving the comma two places to the right or multiplying the quotient by 100)

### Exercises solved

- Find what percent is

a) 10 200 Response: 10^{1}/ 200^{20}= 1/20 = .05 = 5%

b) 24 48 A: 24^{1}/ 48^{2}= 1/2 = 0.5 = 50%

c) 5 40 A: 5^{1}/ 40^{8}= 1/8 = 0.125 = 12.5%

d) 7 84 A: 7^{1}/ 84^{12}= 1/12 = 0.083 = 8.3% - Of the 156 workers in a factory, 142 are engaged in shoe production. What percent of workers are engaged in shoe production?

This problem is solved by calculating what percent is 142 of 156, which is done as follows:

142 ^{71} / 156 ^{78} = 71/78 = .91 = 91%

91% of the workers in this company are engaged in the production of shoes.

## How to Find a Known Number Percent of It

There are situations in which instead of having to calculate the percent of one number or calculate what percent is a number of another, what you need to do is find the number that represents a certain percent of another. One of these situations can be expressed as: “What number is 50% of 40” In this case it is very easy to determine because it is known that 50% of a number is half of it, so here it is simply inferred that 20 is 50% of 40. The situation is complicated when the numbers in question are not so common.

Below we will analyze some examples that demonstrate how to proceed to solve this problem:

Example (6) What number is 12 20% Here the number is unknown and what is known is 18 which is 20% of it. In this case it can be expressed: 20/100 * x = 2 where x is the searched number, then solving for x in the equation would be: x = 12/20/100 applying the rules to divide fractions we obtain: x = 12 ^{3} * 100 ^{20} / 20 ^{5}^{ 1} x = 3 * 20 x = 60

In the demonstration of the previous example it is observed that it is the inverse problem to calculate the percentage of a number, that is why, if in that case it was multiplied, in this it is divided.

It follows that to find a number, given a percent and its result, divide the result by the percent (expressed as a quotient with a divisor of 100). This also results if the result is divided by the Percent and multiply by 100.

For example (7) Find the number of which 15 is 2%.

Applying the above is expressed: = 15 * 15/2/100 100 ^{50} / 2 = 15 * 50 = 750

Using the second way: 15/ 2 * 100 ^{50} = 15 * 50 = 750 So 15 is 2% of 750.

### Exercises solved

- How much is 38 m 50%?

A: 38/50/100 = 38 * 100^{2}/ 50= 38 * 2 = 76 38 m is 50% of 76 m. -
Calculate the number of which:

a) 140 is 70%

Answer: 140/70/100 = 140^{2}* 100/70^{1}= 2 * 100 = 200

140 is 70% of 200 -
b) it is 3.20 4%

A: 3.20 / 4/100 = 3.20 * 100^{25}/ 4^{1}= 3.20 * 25 = 80

20 4% is 80 -
A textile worker has produced 1,959 m of fabric, which is 75% of the plan to be accomplished in one stage. How many meters of fabric will he have produced by completing the stage plan?

Answer: It has the number 1959 and that this is 75% of a number, which is the plan to produce and is not known.

The operation is indicated as follows : 1959/75/100 = 1 959^{653}* 100^{4}/ 75^{2}^{ 1}= 653 * 4 = 2612. The worker will have produced 2,612 meters of fabric by completing the stage plan.

From everything discussed, it can be summarized that three different cases related to the calculation of percent can be presented:

1. Calculate what number is the percent of another. To do this divide

2. Calculate how many percent is a number of another

3. Calculate a number, given another number that is a percent of it.