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Percentage of a Number – Explanation & Examples

The terms percent and percentage are interchangeably used in many situations, but do they mean the same thing?

Well, percent and percentage are slightly different in their usage but they have a similar meaning. Percent or the sign (%) is normally used accompanied by a numerical value. For example, we can say, 95 percent or 95% of the students are bright. Percentage on the other hand is generally used without a number to refer to the word percent. For example, we state that, the percentage of bright students is 95%.

The percentage term was not very old but the method was common. When there was no decimal system, the Ancient Romans used to do calculations of fractions as the multiples of 1/100. For example, they imposed taxes on goods give by the fraction 1/100, which is equivalent to computing percentages. Later in the Middle Ages, the use of 1/100 fraction became more common.

In the 17th century, a standard was set to quote interest rates as 1/100. After its frequent use, the mathematicians abbreviated it as “pc” in 14th century. Later came the term “per”, and finally in 1925, D.E. Smith gave it a symbol form (%).

What is the Percentage of a Number?

Percentage in mathematics is a number or ratio which can be represented as a fraction of 100. The term per cent originates from a Latin word ‘per centum’ which means per 100. The symbol (%) is used to denote percentage.

Similarly, percentage is sometimes denoted by an abbreviation ‘pct.’ For example, we can express 50 percent as 50% or 50 pct. Percentages are written inform whole numbers, fractions or decimals. For example, 4%, 75%, 0.6%, 0.25%, 3/5% etc. are all percentages.

Percentages are part of our daily lives in the following examples:

  • Discounts on commodities are represented in percentages
  • Financial institutions such as banks and SACCOS express the interest charged on loans in form of percentages.
  • Profits and losses are calculated in percentages
  • In academics, percentages are used to evaluate the performance of students
  • The values goods such cars and a piece of land changes with time. This can be represented inform of percentages.

For these reasons, possessing a knowledge on how to calculate percentages is not only helpful for you to excel in mathematics, but also to apply outside the class and solve practical problems involving percentages. This article provides a step by step tutorial on how to calculate percentages.

How to Calculate Percentage?

There are two possibilities of finding the percentage of a number:

  • To find the percentage of a number when it is in decimal form, you just need to multiply the decimal number by 100. For example, to convert 0.5 to a percentage, 0.5 x 100 = 50%.
  • The second case involves a fraction. If the given number is in fractional form, first convert it to a decimal value and multiply by 100. For example, to find the percentage of 1/6: 0.1666 x 100 = 16.7%.

Example 1

Calculate the percentages of the following:

1. 25 of 200?

Solution
(25/200) × 100
Divide the numerator by denominator;
= (1/8) × 100
= (1 × 100)/8
= 100/8
= 25/2
= 12 .5 %

2. 95 out of 150?

Solution
(95/150) × 100
Simplify the fraction and multiply by 100
= (19/30) × 100
= (19 × 100)/30
= 1900/30
reduce the fraction;
= 63 1/3 %

3. 22 of 44?

Solution
(22/44) × 100
Simplify the fraction;
= (1/2) × 100
= (1 × 100)/2
= 100/2
= 50%

4. 30 of 150?

Solution
(30/150) × 100
Simplify the fraction;
= (1/5) × 100
= (1 × 100)/5
= 100/5 = 20%

5. 250 of 1200?

Solution
(250/1200) × 100
Cancel the numerator and denominator;
= (5/24) × 100
= (5 × 100)/24
= 500/24 = 125/6
= 20 5/6 %

6. 86 of 2580?

Solution
(86/2580) × 100
simplify the fraction by cancelling;
= (1/30) × 100
= (1 × 100)/30
= 100/30
reduce the fraction;
10/3
= 3 1/3 %

Example 2

A class has a total of 120 students. Calculate the percentage of girls if they are 60 of them?

Solution

Total number of students in the class = 120

Total number of girls = 60

Therefore, the percentage of girls is calculated as:

(60 × 100)/120

= 600/12 = 50

Hence, 50% of the students are girls.

Example 3

150 students are present in the school auditorium. If the number of boy and girls present in the hall is 80 and 70 respectively. Calculate the percentage of boys present in the auditorium?

Solution

Total number of students present in the auditorium = 150

Number of boys = 80

Percentage of boys = (80 x 100)/150

= 53.33%

 

Practice Questions

1. The number, $1350$, is what percent of $2700$?

2. To the nearest two decimal places, the number, $70$, is what percent of $210$?

3. To the nearest two decimal places, the number, $100$, is what percent of $450$?

4. Out of $500$ marks, James only scored $350$ marks. His brother, Peter, scored $620$ out of $800$ marks. In terms of percentage, who performed better between the two?

5. Christine bought a plot of land with an area of $4000$ squared meters. If she plans to use $2400$ squared meters of the land to construct an apartment complex, which of the following shows the percentage of unused land?

6. Alice runs a fruit shop and just received her restock of $400$ apples and $200$ bananas. Upon close inspecting, $12\%$ of apples and $24\%$ of bananas were rotten. How many percent of the fruits are in good condition?

7. Lorraine has a monthly salary of $\$1200$. If her monthly expenditure on food amounts to $\$480$. What percentage of her monthly salary does she allot for other expenditures and savings?

8. Sam scores $43$ out of $50$ in Mathematics, $62$ out of $75$ in Statistics, and $85$ out of $100$ in Physics. In which subject did he receive the highest percentage score?


 

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