Percentages

Percentages

Introduction

Percentages are fractions that have a denominator always  100. No matter what the numerator is.

Example.

50/100 Is a percentage because the denominator is a hundred. Instead, of writing, a percentage as a fraction we use this ‘%’ symbol.

Real-life situations where we use percentages

1. Calculating Taxes
2. Discount offers
3. To show how much battery is left on the device
4. Interest rates 
5. Sales commission
6. Nutrition values
7. Exam marks

and etc.

Converting a fraction as a percentage

     Why do we convert fractions into a percentage

 because fractions like 10/40, 40/80, 90/120 are hard to compare with each other in the fraction form, But if we convert  the fraction into a percentage it will become easy

 

Converting a fraction into a  percentage

As we know that a percentage is a fraction with  100 as the denominator so we just replace ‘ /100 ‘ with the ‘ % ‘

63 parts out of 100 (whole )

example…

63/100 = 63%

But there is another case where the whole part may not be 100. 

example… 

90/120

A student went to a math test where he scored 90 marks per 120. So to know how much percentage he scored?.

Now write a score as a Fraction (90/120).
Then divide a score(90) by total marks (120). 
And multiply it by a 100 and add the % symbol to the product.

90/120=0.75

0.75 x 100=75

 75 %

The student scored 75%.

Converting a percentage into a fraction

Converting a percentage into a fraction is easy…

we just have to remove the percentage symbol divide by 100 to make it as a fraction. We only have to use a 100, because the percentage calculated based on 100. 
53%→53→53/100

4%→4→4/100 
134%→134→134/100

Converting a percentage into a decimal

Converting percentages into decimals is easy. One way is that the divide the percentage by 100 and the other way is to move the decimal point towards left two places. 

example…

  divide the number percentage by hundred

               75% ÷ 100 = 0.75
              75.5% ÷ 100 = 0.755 
               5% ÷ 100 = 0.05 (need move the decimal point to two places but here in this case ‘5’ is there in one place so used ‘0’ as a placeholder)

Converting a Decimal into a percentage

Converting a decimal into a percentage is easy… we just have to multiply by 100.

3.7865 → 3.7865 x100 → 378.65% (move deimal point  towards right)

0.53→0.53 x 100 →53%
0.04→0,04 x 100 →04% or 4%
1.34→1.34 x 100 →134%

Remember: That you can have percentages more than 100 but the percentage will just become improper and we can also have a decimal percentage. 

Percentage problems

There three main percentage problems we need to know

Finding a percentage

Finding a percentage is easy.

 what is 50% of 60?

so the problem 50% of 60 really means 50% x  60.

Now there are actually two ways to solve this type of problem

one way is using the fraction form of the percentage

and the 2nd way is solving the problem using the decimal form of the percentage.

Way 1: 

here is how to solve the problem using  the fraction form 

1. we should write down the percentage in its fraction form 50/100

2. then we write the other number in its fraction form (in our case 60) 
     60/1

3.  And since we have the term ‘ of ‘ in our problem we replace it with the  ‘x(multiplication)’ symbol
   so now our equation is…
   50/100 x 60/1=?

4. and we multiply the numerators together (50x60=3000) and the denominators together(100x1=100)
   50/100 x 60/1=3000/100

5. now we just have to simplify the fraction (3000/100)
   3000/100=30/1
   30/1=30

6. 50% of 60 is  30.

Way2:

what is 50% of 60
here is how to solve the problem using  the decimal form 

1. we should write down the percentage in its decimal form 0.50

2. then we multiply the normal number the decimal (in our case 0.50 x 60)
   0.50 x 60=30

3. 50% of 60 is 30.

 

What percentage is it?

 

50 is what% of 90?

1. first list the two numbers like a fraction 50/90 (total)

2. Then divide the fraction 50/90=o.55 (rounded 50/90=0.55555555555555555…)

3. now convert the decimal into a percentage (0.55)
   0.55=55%

4. so 50 is 55% of 90               

Missing total

 This the problem when  the total is missing and we have to find the total
here is how…

your friend has some toffies and he says 20% of his toffies are butter-nut
and is there are 8 butter-nut toffies so how many toffies are there altogether

remember: if you see a percentage problem with an ‘altogether’ or ‘total’ or ‘whole’ or ‘in all’ that means you have to do below way…

1. first, we multiply the part by hundred   8 x 100=800

2. then divide the product by the percentage  800÷20=40

3. now we have our answer 40 that means 8 is 20% of 40

remember: that this is how you arrange the equation.

 

The End