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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses applications of percents. By the end of the module students should be able to distinguish between base, percent, and percentage and be able to find the percentage, the percent, and the base.

Section overview

  • Base, Percent, and Percentage
  • Finding the Percentage
  • Finding the Percent
  • Finding the Base

Base, percent, and percentage

There are three basic types of percent problems. Each type involves a base, a percent, and a percentage, and when they are translated from words to mathemati­cal symbols each becomes a multiplication statement . Examples of these types of problems are the following:

  1. What number is 30% of 50? (Missing product statement.)
  2. 15 is what percent of 50? (Missing factor statement.)
  3. 15 is 30% of what number? (Missing factor statement.)

In problem 1 , the product is missing. To solve the problem, we represent the missing product with P size 12{P} {} .

P = 30% 50 size 12{"P "=" 30% " cdot "50"} {}


The missing product P size 12{P} {} is called the percentage . Percentage means part , or por­tion . In P = 30% 50 size 12{"P "=" 30% " cdot "50"} {} , P size 12{P} {} represents a particular part of 50.

In problem 2 , one of the factors is missing. Here we represent the missing factor with Q size 12{Q} {} .

15 = Q 50 size 12{"15 "=" Q " cdot "50"} {}


The missing factor is the percent . Percent, we know, means per 100, or part of 100. In 15 = Q 50 size 12{"15 "=" Q " cdot "50"} {} , Q size 12{Q} {} indicates what part of 50 is being taken or considered. Specifi­cally, 15 = Q 50 size 12{"15 "=" Q " cdot "50"} {} means that if 50 was to be divided into 100 equal parts, then Q indicates 15 are being considered.

In problem 3 , one of the factors is missing. Represent the missing factor with B .

15 = 30% B size 12{"15 "=" 30% " cdot B} {}


The missing factor is the base . Some meanings of base are a source of supply , or a starting place . In 15 = 30% B size 12{"15 "=" 30% " cdot B} {} , B size 12{B} {} indicates the amount of supply. Specifically, 15 = 30% B size 12{"15 "=" 30% " cdot B} {} indicates that 15 represents 30% of the total supply.

Each of these three types of problems is of the form

( percentage ) = ( percent ) ( base ) size 12{ \( "percentage" \) = \( "percent" \) cdot \( "base" \) } {}

We can determine any one of the three values given the other two using the methods discussed in [link] .

Finding the percentage

Sample set a

What number is 30 % of 50 ? Missing product statement. (percentage) = (percent) (base) P = 30 % 50 Convert 30% to a decimal. P = .30 50 Multiply. P = 15

Thus, 15 is 30% of 50.

Do [link] , [link] .

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What number is 36 % of 95 ? Missing product statement. (percentage) = (percent) (base) P = 36 % 95 Convert 36% to a decimal. P = .36 95 Multiply P = 34.2

Thus, 34.2 is 36% of 95.

Do [link] , [link] .

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A salesperson, who gets a commission of 12% of each sale she makes, makes a sale of $8,400.00. How much is her commission?

We need to determine what part of $8,400.00 is to be taken. What part indicates percentage .

What number is 12 % of 8,400.00 ? Missing product statement. (percentage) = (percent) (base) P = 12 % 8,400.00 Convert to decimals. P = .12 8,400.00 Multiply. P = 1008.00

Thus, the salesperson's commission is $1,008.00.

Do [link] , [link] .

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A girl, by practicing typing on her home computer, has been able to increase her typing speed by 110%. If she originally typed 16 words per minute, by how many words per minute was she able to increase her speed?

We need to determine what part of 16 has been taken. What part indicates percentage .

What number is 110 % of 16 ? Missing product statement. (percentage) = (percent) (base) P = 110 % 16 Convert to decimals. P = 1.10 16 Multiply. P = 17.6

Thus, the girl has increased her typing speed by 17.6 words per minute. Her new speed is 16 + 17 . 6 = 33 . 6 size 12{"16 "+" 17" "." "6 "=" 33" "." 6} {} words per minute.

Do [link] , [link] .

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
In the number 779,844,205 how many ten millions are there?
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
Tanis Reply

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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