Definition of percentage :
A Fraction having Denominator 100 is called a Per Cent &
is denoted by symbol %.
# To convert the Fraction into Percentage
To convert a fraction into Percentage, multiply the fraction
by 100 & put % sign.
For Eg: 4/5 à 4/5 * 100 = 80%
# To convert Percentage into a Fraction
To convert a percentage into a fraction replace the % sign
with 1/100 & reduce the fraction to simplest form.
For Eg: 20% à 20/100 = 1/5
# To convert Percentage into Ratio
To convert a percentage into a ratio, first convert the
given percentage into a fraction in simplest form & then to a ratio.
For Eg: 25% à 25/100 = 1/4 = 1 : 4
Important Concepts:
1. 100% of
a Number = Number itself
For eg: 100% of 500 = 500
2. 50% of a number = Half of the number
For eg: 100% of 500 = 500
2. 50% of a number = Half of the number
For eg: 50%
of 500 = 500/2 = 250
3. 25% of a number = Quarter(1/4th) of the number or Half of 50% of the number
3. 25% of a number = Quarter(1/4th) of the number or Half of 50% of the number
For eg: 25%
of 500 will be 500/4 or 250/2= 125
4. To find the 1% of a number, shift the decimal point by 2 place to the left.
4. To find the 1% of a number, shift the decimal point by 2 place to the left.
For
eg: 10% of 500 will be 5.00
5. To find the 10% of a number, shift the decimal point by 1 place to the left.
5. To find the 10% of a number, shift the decimal point by 1 place to the left.
For eg:10%
of 500 = 50.0
6. 5% of the number is half of 10% of a number
6. 5% of the number is half of 10% of a number
For eg:5%
of 500 = 50/2=25
7. 15% of the number = Sum of 10% and 5% of a number
7. 15% of the number = Sum of 10% and 5% of a number
For Eg: 15%
of 500=(10% of 500)+(5% of 500=50 + 2 =75
Using the above methods now we can find the percentage of a
number easily:
Example: 15% of 400 = ?
Example: 15% of 400 = ?
Step 1: Split the percentage term into 2 numbers that
we can easily find the percentage of.
We can split 15% into 10% and 5%
Step 2: First find 10% of 400 by shifting the decimal point to the left by 1 place.
Step 2: First find 10% of 400 by shifting the decimal point to the left by 1 place.
i.e 10% of 400=40.0
Step 3: Now find 5% of 400 i.e half of 10%
Step 3: Now find 5% of 400 i.e half of 10%
i.e 5% of 400=40/2 = 20
Step 4: Now add both the results
Step 4: Now add both the results
we get, 15%+5%=40 + 20 = 60
Therefore, 15% of 400 = 60
Therefore, 15% of 400 = 60
Important Formulas:
1) Percentage
Increase/Decrease:
· If the
price of a commodity increases by R%, then the reduction in consumption so as
not to increase the expenditure is:
= [(R/100+R) * 100]%
= [(R/100+R) * 100]%
· If the
price of a commodity decreases by R%, then the increase in consumption so as
not to decrease the expenditure is:
=[(R/100R) * 100]%
=[(R/100R) * 100]%
2) Population:
If the Population of a town be P
now & it increasing at the rate of R% p.a, then,
· Population
after n years = P[1+(R/100)]^n
· Population n years
ago = P[1+(R/100)]^n
3) Results
on Depreciation
If the present value of a machine is P & it depreciates at the rate of R% per annum. Then:
· Value
of the machine after n years= P[1(R/100)]^n
· Value
of the machine n years ago= P/[1(R/100)]^n
4) If P is R% more than Q, then Q
is less than A by
={ [R/(100+R)]*100}%
={ [R/(100+R)]*100}%
5) If P is R% less than Q, then Q
is more than A by
={ [R/(100R)]*100}%
={ [R/(100R)]*100}%
Learn the Following Table for Fast calculations:
Fraction

Percentage

1/1

100%

1/2

50%

1/3

33.33%

1/4

25%

1/5

20%

1/6

16.66%

1/7

14.28%

1/8

12.5%

1/9

11.11%

1/10

10%

1/15

6.66%

1/20

5%

1/25

4%

1/30

3.33%

1/40

2.5%

1/50

2%

1/60

1.66%

1/75

1.33%

1/80

1.25%

1/90

1.11%

1/100

1%

By Using this Conversion Table we can convert Fraction into
Percentage and Percentage into Fraction easily.
For Eg: To find 3/5 in %?
For Eg: To find 3/5 in %?
Solution: As we have 1/5=20%
then, Multiply both sides by 3
i.e 1/5x3 = 3x20%
Therefore, 3/5 = 60%.