# How To Find the Percentage of a Number – Problems and Solutions | Calculator

### How To Find the Percentage of a Number

CONTENTS:

#### What is a percentage?

A percentage is a fraction which is converted to decimals and then multiplied by 100. The components of a fraction are the numerator and denominator, which are the top number divided by the bottom number respectively. In order to convert a fraction to a percentage, you have to multiply the top and bottom number by the same factor which converts the denominator to 100.

For example, let’s convert ¼ to a percentage. Using the two methods already explained above:

Method 1

Step 1 – Convert ¼ to decimals >> ¼ = 0.25

Step 2 – Multiply 0.25 by 100 >> 0.25 x 100 = 25%

Method 2

Step 1 – We have the fraction (¼). The numerator is 1 and the denominator is 4.

Step 2 – Convert the denominator to 100. Using ratios, 4 is equivalent to 100

Step 3 – Convert the numerator to X (unknown value). Using ratios, 1 is equivalent to X

Step 4 – Using proportions to find the value of X,

If 4 = 100, then 1 must be less than 100, therefore to find X, we set up the following proportional equation:

4 =100

1= X

X = (1 x 100)/4

X = 25

### Simple Percentage Problems in Mathematics:

#### Examples of Percentage Calculations

• Express 3/5 as a percentage
• What is 3% of 35?
• What percent of 80 is 20?
• 12 is 5% of what number?

### How To Convert Fraction to Percentage?

Using the proportional equation which we derived much earlier, we can make substitutions to come up with a general equation that can be used to calculate unknown values.

The specific proportional equation X = (1 x 100)/4 was used to convert the fraction (1/4) into a percentage. We can derive a general proportional equation by making substitutions:

X = (N * 100)/D,

Where X = percentage

N=numerator

D=denominator.

The equation can be re-arranged as you wish:

X = (N/D)*100

(N/D) is the fraction you want to convert to a percentage.

Let’s use the above equation to solve the following problems:

Problems

Express the fraction 3/5 as a percentage.

Solution – From the equation X=(N/D)*100, N=3 and D=5, therefore X=(3/5)*100 = 60%

Express the fraction 1/3 as a percentage.

Solution – From the equation X=(N/D)*100, N=1 and D=3, therefore X=(1/3)*100 = 33%

How To Find the Percentage of a Whole Number?

Previously we talked about fractions which are expressed as (N/D) where N=numerator, and D=denominator. The opposite of fractions are whole numbers. A whole number only contains a numerator and its denominator is always 1. For example 5/1 = 5, 10/1 = 10, 13/1 = 13 and 25/1 = 25.

To find the percentage of a whole number, we should first convert the percentage to a fraction, then multiply the fraction by the whole number as shown in the examples below:

Problem 1

What is 3% of 35?

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Step1 – Convert 3% to a fraction >> 3/100

Step 2 – Multiply the fraction by the whole number >> (3/100)*35

>> (3/100)*35

>> (3/20)*7

>> (21/20) = 1.05

Answer: 3% of 35 = 1.05

The specific equation in this case is (3/100)*35=1.05

We can convert this equation to a general equation by substituting values as shown below:

(N/D)*W=P, where N=numerator, D=denominator, W=whole number and P=dividend of whole number.

We can use this specific formula to find the percentage of any whole number:

Problem 2

What is 75% of 50?

Using the formula (N/D)*W=P,

P=(N/D)*W

Convert 75% to a fraction >> 75%=75/100,

P=(75/100)*50

>> P=(3/4)*50

>> P=37.5

Answer: 75% of 50 = 37.5

### How To Find the Percentage of Two Numbers?

P=(N/D)*W, where N=numerator, D=denominator, W=whole number and P=dividend of whole number.

We can use the same formula P=(N/D)*W to find the unknown percentage of two numbers.

Problem 1

What percent of 80 is 20?

Step 1 – Express the numbers as fractions >> 20/80

Step 2 – Multiply the fraction by 100 >> (20/80)*100 = (2/8)*100 = (1/4)*100 = 25

Alternatively, we can use the formula P=(N/D)*W,

W=80,

P=20,

Therefore we need to find (N/D),

D=100,

Making substitutions, the formula becomes 20=(N/100)*80,

>> 20=(N/100)*80

>> 20=(N/10)*8

>> 20=(N/5)*4

Dividing both sides by 4:

>> 5= N/5

Multiplying both sides by 5:

>> 25 = N,

Therefore N=25

Answer: 20 expressed as a percentage of 80 is 25%

### How to Find the Whole Number from a Percentage?

P=(N/D)*W, where N=numerator, D=denominator, W=whole number and P=dividend of whole number.

This same formula can be used to find the whole number from a percentage.

Problem 1

12 is 5% of what number?

Step 1 – Express the percentage as a fraction 5% >> 5/100

Step 2 – W is the unknown whole number, P= 12, N=5 and D=100

Step 3 – Make substitutions inside the formula P=(N/D)*W >> 12=(5/100)*W

12 = (5/100)*W

12 = (1/20)*W

W = 12/(1/20)

W = 12*20

W = 240

Answer: 12 is 5% of 240.

Alternatively, you can set up a logical equation to solve X the unknown number:

5% of X = 12

Therefore,

>> (5/100)*X = 12

>> (1/20)*X = 12

>> X/20 = 12

Multiplying both sides by 20:

>> X = 240.

Answer: 12 is 5% of 240.

### Examples of Percentages in Real Life – Problems and Solutions

Percentages are found and used in a wide variety of fields such as mathematics, statistics, physics, chemistry, food processing, engineering, technology, business, finance, economics, marketing, administration, accounting, programming, meteorology, sports, politics and construction. The examples below illustrate the importance of percentages in our daily life.

#### Problem 1 – Percentages in Website Traffic Analysis:

According to a website traffic analysis tool, 20.42% of visitors on Tiktok are from the United States, 7.23% are from the Philippines, 5.94% are from the Vietnam, 5% are from Mexico and 4.68% are from Russia. The rest are from other countries. Find the percentage of visitors from other countries?

Calculations:

Step 1 – Add 20.42 + 7.23 + 5.94 + 5 + 4.68 = 43.27%

Step 2 – Subtract the sum from 100% >> 100-43.27 = 56.73%

Answer: 56.73% of visitors are from other countries.

Question 2:

If Tiktok gets 1.34 billion visitors a month, how many visitors are from the USA?

Calculations:

20.42% of visitors are from the USA, so 20.42% of 1,340,000,000 = 0.2042 x 1.340,000,000 = 273,628,000

Answer: 273,628,000 visitors are from the USA.

#### Problem 2 – Percentages in Politics & Elections:

In the US presidential elections held On 7 November 2012, Barack Obama got 59,631,249 popular votes representing 50% of all votes and Mitt Romney got 57,000,976 votes representing 48% of all votes.

1. Find the percentage of voters who didn’t vote for either candidate?

Calculations:

Step 1 – Add 50 + 48 = 98%

Step 2 – Subtract the total from 100% >> 100 – 98 = 2%

Answer: 2% of voters didn’t vote for either candidate.

1. Find the total number of voters?

Calculations:

Step 1 – Create an equation from known and unknown values. Let X be the total number of voters >> 59,631,249 + 57,000,976 = 98% of X >> 116,632,225 = 0.98X

Step 2 – Solve for X >> 0.98X = 116,632,225

>> X = 116,632,225/0.98

>> X = 119,012,475

Answer: The total number of voters was 119,012,475

#### Problem 3 – Percentages in Technology:

A laptop battery is discharging (losing energy or voltage) at a constant rate, with 2 hrs 45min (97%) of energy remaining. What will be the percentage of energy remaining after 1 hour? Windows Battery Meter – Practical real life applications of percentages

Calculations:

Step 1 – Convert the time to minutes, thus >> 2 hrs 45 min = 165 min and 1 hour = 60 minutes.

Step 2 – To find the battery time (energy) remaining after 1 hour >> 165 – 60 = 105 minutes.

Step 3 – Using ratios >> 165 min is equivalent to 97% of energy remaining, 105 minutes is equivalent to X% of energy remaining.

If 165 min = 97%, then 105 min must be less than 97%, therefore to find X, we set up the following proportional equation:

165 = 97%

105 = X

X = (105 x 97)/165

X = 10185/165

X = 61.73

Answer – 61.73% will be the percentage of energy remaining after 1 hour.

Method 2:

Let y be the total time it takes to discharge the battery to zero capacity,

97% of y = 165 min

0.97y=165

y = 165/0.97

y = 170.1

Therefore, the percentage of energy remaining after 1 hour is:

105 /170.1 = 0.6173

Converting the decimals to percentage >> 0.6173 x 100 = 61.73%

#### Problem 4  – Percentages in Technology:

The full size of a picture is 350×350 pixels when zoomed to 100%. What is the size of the picture when zoomed to 40%? Microsoft Office Picture Manager – Practical real life applications of percentages

Method 1:

40% of 350 >> 0.4 x 350 = 140

Answer: the size of the picture is 140 x 140 pixels when zoomed to 40%

Method 2:

Using ratios >> 100% is equivalent to 350 pixels, and 40% is equivalent to X%.

If 100% = 350 pixels, then 40% must be less than 40%, therefore to find X, we set up the following proportional equation:

100% = 350

40% = X

X = (40 x 350)/100

X = 14000/100

X = 140

Answer – the size of the picture is 140 x 140 pixels when zoomed to 40%.

#### Problem 5  – Percentages in Food Production:

500g of margarine contains 80% of vegetable fats and oils, and 16.7% of water. The rest of the ingredients are salt, milk, whey powder, emulsifiers, lecithin, preservatives, vitamins, citric acid, flavouring and colorants.

What is the percentage of other ingredients?

Solution:

x = Amount of fats and oils in margarine.

y = Amount of water in margarine.

z = Amount of other ingredients

t = Total amount

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x + y + z = t

Making substitutions:

>> 80 + 16.7 + y = 100

>> 96.7 + y = 100

>> y = 100 – 96.7 = 33

Answer: the percentage of other ingredients is 33%

What is the mass of other ingredients in grams?

Solution:

>> x = 80% of 500g = 0.80 x 500g = 400g

>> y = 16.7% of 500g = 0.167 x 500g = 83.5g

>> x + y = 483.5g

>> t = 500g

Therefore,

>> z = t – (x + y)

>> z = 500 – 483.5 = 16.5g

>> z = 16.5g

Answer: the mass of other ingredients is 16.5g

What is the mass of vegetables and oils in the margarine?

Solution:

>> x = 80% of 500g = 0.80 x 500g = 400g

Answer: the mass of vegetables and oils is 400g.

What is the mass of water in the margarine?

Solution:

>> y = 16.7% of 500g = 0.167 x 500g = 83.5g

Answer: the mass of water is 83.5g.

The full size of a Noxplayer setup file is 499MB. If you are downloading the file at a constant internet speed, what percentage of the file is 10.6MB? Solution:

Method 1:

X% of 499MB = 10.6MB

>> (X/100)*499 = 10.6MB

Multiplying both sides by 100:

>> 499x = 1060

>> x = 1060/499

>> x = 2.12

Answer: 2.12% of the file is 10.6MB

Method 2:

Using ratios >> 100% is equivalent to 499MB,and X% is equivalent to 10.6MB.

If 100% = 499MB, then X% is less than 100%, therefore to find X, we set up the following proportional equation:

100% = 499

X% = 10.6

X = (10.6 x 100)/499

X = 2.12

Answer: 2.12% of the file is 10.6MB

#### Problem 6  – Percentages in Commerce:

A man went to the shops to buy some groceries. His receipt shows a total sum of \$154.33 after tax . Value Added Tax (VAT) at 15% was charged on \$66.37 worth of groceries. Calculate the amount of VAT and subtotal before tax?

Solution:

VAT = 15% of \$66.37 = 0.15 x \$66.37 = \$9.96

Subtotal before tax >> \$154.33 – \$9.96 = \$144.37

#### Problem 7  – Percentages in Concrete Volumetric Mix Ratios:

The prescribed mix for concrete class B (15MPa) is 1:3:5 representing cement, sand and gravel. The quantity of concrete cast is 4.89m3. Calculate the percentage and quantity of sand in the concrete?

Solution:

The total of the ratio 1:3:5 = 9,

Therefore (3/9) x 100 = 33%

The percentage of sand in the mix is 33%

33% of 4.89m3 = 0.33 x 4.89 = 1.69m3

The quantity of sand in the mix is 1.69m3

#### Problem 8  – Percentages in Acoustics:

If 10 db is twice the loudness, by how much percent was the volume increased if the sound is 60 db?

Solution:

>> Twice the loudness is equivalent to (2/1) x 100 = 200%

>> Therefore 10 db = 200% increase

Using ratios: If 10 db = 200%, then 60 db is more than 200%,

Setting up a proportional equation:

10 db = 200%

60 db = X%

X = (60/10) x 200 =1200% increase

Answer: The volume was increased by 1200% Audio and Video Player Software – Practical real life applications of percentages 