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Mathematic – Percentage Calculation

by Lau Hao Ying
(Singapore)











































In a school of 1800 pupils, 324 pupils wear glasses. What percentage of the pupils
do not wear glasses?

Comments for Mathematic – Percentage Calculation

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Oct 08, 2012
Percentage Calculation
by: Staff

Answer:

Part I

Calculate the number of pupils who do not wear glasses

(Pupils who wear glasses) + (Pupils who DO NOT wear glasses)
= (Total number of pupils)

324 + (Pupils who DO NOT wear glasses) = 1800

(Pupils who DO NOT wear glasses) = 1800 - 324

(Pupils who DO NOT wear glasses) = 1476




Pupil and Glasses Summary

Pupils who wear glasses = 324

Pupils who DO NOT wear glasses = 1476

Total number of students = 1800


What percentage of the pupils do not wear glasses?

                  number without glasses
% NO GLASSES = -------------------------- * 100
total number of students

1476
% NO GLASSES = ------- * 100
1800

% NO GLASSES = 82 %


The final answer is: 82%


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The question you may be asking yourself about now is probably something like this:

Why not just use the numerical total for the number of pupils who DO NOT wear glasses? 1476 pupils is straightforward and easy to understand.

This is why:

Percents are a CONVENIENT WAY to EXPRESS a PROPORTION.

Calculating a percent may be extra work. However, once the percent calculation has been completed, PERCENTS are EASY TO UNDERSTAND and EASY TO USE.


PERCENTS are EASY TO UNDERSTAND

For example, suppose two students have the following academic averages: 84% and 86%.

It is easy to see that (all other things being equal) the student with the 86% average is the better student. All anyone has to do is look at the numbers. 86% is a bigger number than 84%. 86% is better than 84%.

Even if the person reading the two numbers (84% & 86%) has no idea how a percent is calculated, they still understand that 86% is bigger and better than 84%.



What percents actually mean:

I will continue to use the example of the two students who earned the 84% and 86% averages.

For this example, the students earned their percentage scores entirely from multiple choice tests.

(Students in the real world do more than just take multiple choice tests. However, for this example that’s all they do.)

84% means that for every 100 multiple choice questions this student attempted to answer, this student answered 84 correctly.

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Oct 08, 2012
Percentage Calculation
by: Staff


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Part II


86% means that for every 100 multiple choice questions this student attempted to answer, this student answered 86 correctly.

By now you are probably thinking: Students’ are not given tests with exactly 100 questions every time. What about a student that is given a test with only 75 questions, or the student who is given a test with 150 questions?

A % calculation compensates for these differences. That is one reason a percent calculation is so practical.

However, the most STRAIGHTFORWARD way to represent a PROPORTION is to USE a FRACTION.



For example, suppose the first student in the example actually took a test with only 75 questions and answered 63 questions correctly.

The proportion of questions answered correctly can be represented by the fraction 63/75 (63 correct answers out of 75 questions).

Now suppose the second student in the example actually took a test with 150 questions and answered 129 questions correctly.

The proportion of questions answered correctly can be represented by the fraction 129/150 (129 correct answers out of 150 questions).

Which student is the best student?

Compare the fractions.

Which student has the highest average (which is the larger fraction)? 63/75 or 129/150?

It is very hard to answer that question by merely glancing at these fractions.

Writing fractions to represent a proportion may be easy, but comparing different fractions can be frustrating and time consuming.


Using a percent to compare two proportions does not have this difficulty.

Comparing two percents is easy to do. That is one of the reasons a percent is normally used instead of a fraction.


(However, remember that a fraction and a percent both REPRESENT exactly the same thing: a PROPORTION.)


PERCENTS are EASY TO USE

Percents are used in many types of calculations.

For example, suppose the government imposes an 8% sales tax on the items you purchase. This means that for every dollar you spend, you owe an additional 8 cents in sales tax.

That tax is expressed as a percentage because different people spend different amounts of money. The tax on different amounts of money will be different.

Suppose person “A” spends $51. How much sales tax do they owe? (The decimal equivalent of 8% is 0.08)

Calculation of Sales Tax for person “A”: $51 * .08 = $4.08

Suppose person “B” spends $16. How much sales tax do they owe?

Calculation of Sales Tax for person “B”: $16 * .08 = $1.28



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Oct 08, 2012
Percentage Calculation
by: Staff

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Part III




How to CALCULATE a PERCENT

How to calculate a percent:


Calculating a percent requires a small amount of work.

Calculating a percent means the fraction (which represents the proportion) must be converted to a decimal, and then the decimal must be multiplied by 100.

To complete this process: use a calculator or be prepared to do some division long hand.

Converting the two fractions to percents: 63/75 and 129/150

Percent – 1st student

Proportion = 63/75

= (63/75) * 100

= (.84) * 100

= 84 %


Percent – 2nd student

Proportion = 129/150

= (129/150) * 100

= (.86) * 100

= 86 %



Thanks for writing.

Staff
www.solving-math-problems.com



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