So you want to learn about the basics of Percentage? Click [[here->Percentage Intro]]
Heh. I don't need to learn about basic Percentage. Take me directly to the [[problem set->Problem Set Intro]].//You must have definitely encountered percentage in your day-to-day life, whether when checking the battery level in your phone, the marksheet in a grade card at the end of a term, or in many different situations.
//
(text-style:"fade-in-out")[''Try to think of a situation where you have used the term percentage.'']
But the question remains: ''What'' is [[Percentage->The symbol %]]?The Symbol "''%''" is read out as ''PER-CENT''.
(text-style:"buoy")[It comes from the Latin //Per// (which means ratio of) and //Centum// (the Latin root of century i.e 100).]
So this symbol refers to a ratio with respect to a ''standard number'' which is always ''100''.
So, for instance, 35% is read out as "THIRTY FIVE PERCENT"
And, it refers to the ratio 35:100 or 35/100.
[[Let us try a question to test this knowledge->% Q]]What ratio is 67% ? (dropdown: 2bind $Ans,"6:7","67:1","67:10","67:100")
(live:)[(if: $Ans is "67:100" )[[[Proceed!->Ratio simplify]] Well done!(stop:)](else:)[Check your answer again]]So we see that percentage is a //special// type of ratio where the denominator is a special number ''100''.
(text-style:"buoy")[In other words EVERY PERCENTAGE IS A RATIO!]
And this ratio can be simplified by removing the common factors to get the irreducible proportion, just like any ratio.
For example 35: 100 = 35 / 100 = 7x5 / 20x5 = 7/20 ( the irreducible form)
[[Let us test this with a question->Ratio Q]]What is the irreducible ratio form of 25%?
(input-box:2bind $An2,"=XX=","Answer in a:b form")
(live:)[(if:$An2 is "1:4")[[[Proceed!->ratio 2 percentage]] Well done(stop:)](else:)[Check your answer]]We have seen that we can convert percentages to ratios (by dividing with 100). How about the reverse question: can we convert a ratio into a percentage?
[[Yes we can->Rat 2 Perc]]
[[No we can't do this. What a stupid idea!->Change your mind]]The algorithm to convert a ratio to a percentage is just the ''reverse'' of the previous idea.
To convert a % to ratio, we divided by 100.
(text-style:"sway")[We convert a ratio into a percentage by //multiplying// by 100.]
For example, 3:5 can be converted into a percentage as follows:
3/5 x 100 = 3 x 20 = 60%
[[Let us test this out with a question.->Rat 2 Perc Q]]Yes, it does seem a little unlikely, but perhaps we can change your mind.
Let me [[try->Rat 2 Perc]]What is the percentage equivalent of the ratio 2:25?
(dropdown: 2bind $An3,"2%","8%","25%","50%")
(live:)[(if:$An3 is "8%")[[[Proceed!->Conclusion]] Excellent job(stop:)](else:)[Hmm...Check your answer]]So we can conclude that every percentage can be converted into a ratio
(text-style:"fade-in-out")[//[''METHOD'': divide the percentage by 100, and remove common factors]//]
And also that every ratio can be converted into a percentage.
(text-style:"fade-in-out")[//[''METHOD'': multiply the ratio with 100 and simplify]//]
In other words, every ratio can be written as a percentage and every percentage can be written as a ratio.
RATIOS AND PERCENTAGES ARE (t8n-depart:"dissolve")+(t8n-arrive:"zoom")+(t8n-time:1.5s)[[INTER-CONVERTIBLE->interconvertible]]!
[[Now that we know this,let us have some fun with the Problem set and test this out->Problem Set Intro]]Keep a pencil/pen and some paper ready: It's time to solve problems!
Would you like some [[problems with numbers->Num Prob]] to warm up?
Or do you want to do [[word problems->Word Prob]] instead?
Or perhaps, you'd like that [[introduction to Percentages->Percentage Intro]] after all?
[[EXIT->Exit]] is this wayWhich Problem would you like?
[[Problem No 1->NP1]]
[[Problem No 2->NP2]]
[[Problem No 3->NP3]]
[[Problem No 4->NP4]]
[[Problem No 5->NP5]]
OR perhaps you would like that [[introduction to Percentage->Percentage Intro]] after all
Or click here to go to [[word problems->Word Prob]]
Click [[here->Assignment]] to see the AssigmentWhich Problem would you like?
Sample Problem 1: Read [[this->WPS]] first
Sample Problem 2:Read [[this->WPS2]] next
[[Word Problem No 1->WP1]]
[[Word Problem No 2->WP2]]
[[Word Problem No 3->WP3]]
OR perhaps you would like that [[introduction to Percentage->Percentage Intro]] after all
Or click here to go to [[Number Problems->Num Prob]]
Assignment problems are [[this way->Assignment]]
Click [[here->Exit]] to EXITHopefully, the link between ratios and percentages are clear now.
You can visit this page whenever you want to refresh this topic!
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Let us explore the concept of percentage
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Would you like to [[Proceed->Percentage page]]?
Or perhaps it's time to [[exit->Exit]]Convert 4:5 into a percentage
(dropdown: 2bind $Annp1,"4%","40%","80%","50%")
(live:)[(if:$Annp1 is "80%")[[[Proceed!->NP2]] Excellent job
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->NP1Ans]] to see an explanation of the answer
(stop:)](else:)[Hmm...Check your answer]]Convert 80% into an irreducible ratio
(dropdown: 2bind $Annp2,"80:100","8:10","8:1","4:10","4:5")
(live:)[(if:$Annp2 is "4:5")[[[Proceed to next problem!->NP3]] Excellent job.
Click [[here->Num Prob]] to return to the Number Problems List
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->NP2Ans]] to see an explanation of the answer
(stop:)](else:)[Hmm...Check your answer]]Check the box if TRUE: 5:10 is equivalent to 50%
(checkbox: 2bind $Annp3,"True")
(live:)[(if:$Annp3 is true)[[[Proceed to next problem!->NP4]] Excellent job.
Click [[here->Num Prob]] to return to the Number Problems List
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->NP3Ans]] to see an explanation of the answer
(stop:)](else:)[Hmm...Check your answer]]Convert 52% into an irreducible ratio
(dropdown: 2bind $Annp4,"52:100","26:50","13:25","4:5")
(live:)[(if:$Annp4 is "13:25")[[[Proceed to next problem!->NP5]] Excellent job.
Click [[here->Num Prob]] to return to the Number Problems List
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->NP4Ans]] to see an explanation of the answer
(stop:)](else:)[Hmm...Check your answer]]Check the box if TRUE:
3:10 is smaller than to 50%
(checkbox: 2bind $Annp5,"True")
(live:)[(if:$Annp5 is true)[[[Proceed to word problems->Word Prob]] Excellent job.
Click [[here->Num Prob]] to return to the Number Problems List
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->NP5Ans]] to see an explanation of the answer
(stop:)](else:)[Hmm...Check your answer]]Saroj scores 768 marks out of 800. What is her percentage?
ANS: 96%
EXPLANATION: First we convert the score into a ratio. 768/800 = 24/25
This can be converted into a percentage by multiplying with 100.
Hence her percentage is 24/25 x 100 = 96%
Click [[here->Word Prob]] to return to the Word Problem Set
Click [[here->WPS2]] to see another sample problem.Ana scores 67% in her test. If the maximum marks in the test was 500, how many marks did Ana score?
ANS: 335
EXPLANATION: Let Ana score m marks. Then the ratio of her marks is m/500.
On the other hand her percentage is 67% which is equivalent to 67/100.
These ratios must be equal (as the percentage is equivalent to her mark-ratio)
Hence, m/500 = 67/100.
We can solve this by multiplying both sides with 500 to get
m= 67/100 x 500 = 67 x 5 = 335
Click [[here->WP1]] to go to the first Word Problem.
Click [[here->Word Prob]] to return to the Word Problem SetThere are 42 boys and 18 girls in a class. What is the percentage of boys in the class?
(input-box:2bind $Anwp1,"=XX=")
(live:)[(if:$Anwp1 is "70")[[[Proceed!->WP2]] to the next problem. Well done
Click [[here->Word Prob]] to return to the Word Problems List
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->WP1Ans]] to see an explanation of the answer
(stop:)](else:)[Check your answer]]Gunpowder contains 15% charcoal. Find quantity (in grams) of charcoal in 8000g of gunpowder?
(input-box:2bind $Anwp2,"=XX=")
(live:)[(if:$Anwp2 is "1200")[[[Proceed!->WP3]] to the next problem. Well done
Click [[here->Word Prob]] to return to the Word Problems List
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->WP2Ans]] to see an explanation of the answer
(stop:)](else:)[Check your answer]]In a class of 60 students, 15% remained absent on a rainy day. How many pupils were present in the class on that day?
(dropdown: 2bind $Anwp3,"6","9","51","15","20","54","45")
(live:)[(if:$Anwp3 is "51")[[[Proceed!->Assignment]] to Assignment page. Well done! Have fun with the assignments!
Click [[here->Word Prob]] to return to the Word Problems List
and (t8n-arrive:"dissolve")+(t8n-time:3s)[[here->WP3Ans]] to see an explanation of the answer
(stop:)](else:)[Check your answer]]''(align:"=><=")+(box:"X=")[ASSIGNMENT]''
''These problems are for testing yourself and self-study. ''
1) 28% of a number is 42. Find the number
2) Anakin attempted an exam whose total marks is 850. He gets 34% and fails by 17 marks. Find the passing mark of the exam.
3) 1200 boys and 600 girls wrote an exam. 42% of boys and 30% of girls passed the exam. Find the percentage of those who failed.
4) Express 65p as a percentage of Rs.5.
''NOTE'': //SOLUTION IS ''NOT'' INCLUDED//.
Click [[here->Exit]] to exit.//''Inter-convertible'' means we can convert one into the other and reverse aslo//
We know that ratio can be converted into percentage
Percentage can be converted into ratio.
This shows that they are interconvertible
(t8n-time:1.5s)[[Click here to return to the previous page->Conclusion]]ANSWER:
80% = 80/100
= 4 x 20 / 5 x 20 ..... (text-style:"fade-in-out")[common factor is 20]
= 4 / 5
= 4 : 5
''NOTE:'' Comparing the answers from previous problems we see that converting from a ratio and percentage to back again gives us the original ratio.
Click (t8n-time:3s)[[here->NP3]] to go to to the next problem.ANSWER:
4:5 = 4/5
To convert into a percentage we multiply by ''100''
= 4 x 100 / 5
= 400/5
= 80 ..... (text-style:"fade-in-out")[performing the division]
= 80%
Click (t8n-time:3s)[[here->NP2]] to go to to the next problem.ANSWER:
5:10 = 5/10 x 100
= 500/10
= 50 ..... (text-style:"fade-in-out")[performing the division]
= 50%
Hence, the statement is ''TRUE''
Click (t8n-time:3s)[[here->NP4]] to go to to the next problem.ANSWER:
52% = 52/100
= 13 x 4 / 25 x 4 ..... (text-style:"fade-in-out")[common factor is 4]
= 13/25
= 13:25
Click (t8n-time:3s)[[here->NP5]] to go to to the next problem.ANSWER:
Consider 3:10
Let us convert this into a percentage
3:10 = 3/10 x 100
= 300/10
= 30..... (text-style:"fade-in-out")[performing the division]
= 30%
By comparing 30% to 50% we see that it is smaller.
Click (t8n-time:3s)[[here->Word Prob]] to go to to the next section.ANSWER:
We first consider the total number of students.
The total number of students come from the boys and girls put together, henceit is 42+18
Total number of students = 60 students.
Now the ratio of boys in the class is given by 42/60
= 7 x 6 = 10 x 6 ..... (text-style:"fade-in-out")[common factor is 6]
= 7/10
Finding percentage is done by multiplying this with 100, to get
700/10
=70
=70%
Click (t8n-time:3s)[[here->WP2]] to go to to the next problemANSWER:
We first find the ratio of gunpowder.
Gunpowder contains 15% charcoal, hence
15% = 15 /100
= 3 x 5 / 20x5 ..... (text-style:"fade-in-out")[common factor is 5]
= 3/20
Since this must be the same ratio even for 8000g of gunpowder, the amount of charcoal in 8000g is nothing but
3/20 x 8000
= 24000/20
= 1200g
Click (t8n-time:3s)[[here->WP3]] to go to to the next problemANSWER:
We first consider 15% as a ratio.
We have seen that 15% is 3/20
Hence in a class of 60 students, 15% of the students is given by:
3/20 x 60 = 180 / 20
= 9
This means that 9 students were absent, this implies that
60 - 9 = 51 students were present
Click (t8n-time:3s)[[here->Word Prob]] to return to to the section