Finding Percentage in
your head
Percentage is merely a two place decimal without the
decimal point shown. Percent has its origin from the Latin word per centum meaning per hundred. It can
best be defined as: - A fraction whose denominator is 100 is called a
percentage and the numerator of the fraction is called the rate percent.
The importance of percentage can be estimated with
the fact that whether you go to Bank for taking loan or go to shopping mall for
buying something you always feel the importance of calculating percentage. Let’s
take some example to understand the importance of percent in daily life.
a) If the bank offers you the interest rate of home
loan @10% per annum it simply means that you have to pay ` 10 per ` 100.
b) Suppose while reading newspaper early in the
morning you get an ad claiming that you will get 50% + 50% off on buying a pair
of jeans and in the evening you rush to the shop in a hope you will get 100% discount
on jeans then you are really thinking it other way because you have
miscalculated the percentage discount the company or shop is offering you.
c) We all know that in order to get 1st
Division in School/ College examination you need to acquire 60% marks of the
total.
It is not all, in every competitive examination you
appear; you encounter some problem on percentage directly or indirectly.
This altogether shows that it is an important tool
for our life. Here I shall not deal with the typical problem asked in
examination involved percentage which comes in the form of Profit and Loss,
Simple or Compound Interest etc. but I shall simply show you the way how you
can calculate the simple percentage.
This clearly shows the importance of percentage. 1 %
of a number is 1/100 of the number; 15% of a number is 15/100 and so on. This
reminds me a question which is crucial in primary level and is used to some
extent in senior or competitive level – what percent one number is of other.
Let me explain it before I move to the main discussion.
What
percent one number is of other?
Follow
these simple steps and get the answer in your mind.
·
Put the number
that follows the word what percent is in
the numerator of the fraction
·
Place the other
number to the denominator of the fraction.
·
Reduce the
fraction in simplest part if possible and finally multiply the result by 100.
Example;
- What percent is 16 of 80?
Solution:
- Place 16 in numerator and 80 at denominator and multiply the fraction by 100.
Example:
What percent is 36 of 4?
Solution:
- Place 36 at the numerator and 4 at the denominator and multiply the result by
100
Let’s
learn some special technique to find a certain percentage of a number. These
method will give you an edge to do the calculation fast.
Finding
2 ½ % of a number
Suppose you are asked to find 2 ½ % of a number you
will simply convert it into a fraction and multiply the number by 5/2 and
divide it by 100 but this will take undoubtedly a minute from you. Let’s learn
some simple trick and do it in your mind.
1.
Divide the
number whose 2 ½ % you are going to calculate by 4
2.
Move decimal
point one place to left.
Hey, did you get the answer? Of course, YES. Isn’t
it super simple?
Let me take some examples to put focus on its
working.
Example: Find 2 ½ % of 86
Solution: -
Divide 86 by 4; 86 ÷ 4 = 21.5 Move decimal point one place to left =
2.15
Hence, 86 × 2 ½ % = 2.15
Example: Find 2 ½ % of 648
Solution: -
Divide 648 by 4; 648 ÷ 4 = 162 Move decimal point one place to left =
16.2
Hence, 648 × 2 ½ % = 16.2
Finding
5% of a number
Let me ask you a simple question: - Are you
comfortable dividing a number by 2? Your answer is a big YES. Finding 5% of a
number is as simple as dividing a number by 2. Let’s see how it works.
1.
Divide the
number by 2
2.
Move the decimal
point one place to left
Example: - Find 5% of 850
Solution: - Divide 850 by 2; 850 ÷ 2 = 425
Move decimal point one place to left =
42.5
Hence, 850 × 5% = 42.5
Example: - Find 5% of 326
Solution: - Divide 326 by 2; 326 ÷ 2 = 163
Move decimal point one place to left =
16.3
Hence, 326 × 5% = 16.3
Finding
10% of a number
Finding 10% of a number is a child’s play. You
follow the simple steps and get the answer in second.
1.
Simply Move the decimal point one place to
left
Example: - Find 10% of 729
Solution: - Move decimal point one place to left =
72.9
Hence, 729 ×10% = 72.9
Example: - Find 10% of 2549
Solution: - Move decimal point one place to left =
254.9
Hence, 2549 ×10% = 254.9
Finding
15% of a number
If I ask you to multiply a number by 2 then you will
comfortably do it. If I again ask you to divide a number by 2 then also you
will get your answer correct. That all you have to do in order to find 15% of a
number. Follow the steps.
1.
Divide the
number by 2
2.
Multiply the
result obtained by 3
3.
Move the decimal
point one place to left
Example: - Find 15% of 43
Solution: - Divide 43 by 2; 43 ÷ 2 = 21.5
Multiply it by 3 = 21.5 × 3 = 64.5
Move decimal point one place to left = 64.5
Hence, 43 × 15% = 64.5
Example: - Find 15% of 438
Solution: - Divide 483 by 2; 438 ÷ 2 = 219
Multiply it by 3 = 219 × 3 = 657
Move decimal point one place to left =
65.7
Hence, 438 × 15% = 65.7
Finding
20% of a number
Follow the
steps.
1.
Divide the
number by 5
Example: - Find 20% of 43
Solution: - Divide 43 by 5; 43 ÷ 5 = 8.6
Hence, 43 × 20% = 8.6
Example: - Find 20% of 348
Solution: - Divide 348 by 5; 348 ÷ 5 = 69.6
Hence, 348 × 20% = 69.6
Finding
25% of a number
Follow the steps.
1.
Divide the
number by 4
Example: - Find 25% of 86
Solution: - Divide 86 by 4; 86 ÷ 4 = 21.5
Hence, 86 × 25% = 21.5
Example: - Find 25% of 484
Solution: - Divide 484 by 4; 484 ÷ 5 = 121
Hence, 484 × 25% =121
Finding
33 1/3 % of a number
Follow the steps.
1.
Divide the
number by 3
Example: - Find 33 1/3% of 69
Solution: - Divide 69 by 3; 69 ÷ 3 = 23
Hence, 69 × 33 1/3 % = 23
Example: - Find 33 1/3 % of 921
Solution: - Divide 921 by 3; 921 ÷ 3 = 307
Hence, 921 × 33 1/3 % = 307
Finding
40 % of a number
Follow the steps.
1.
Multiply the number
by 4
2.
Move decimal one
point left
Example: - Find 40% of 24
Solution: - Multiply the number by 4: 24×4 = 96
Move decimal one point left = 9.6
Hence, 24 × 40 % = 9.6
Example: - Find 40% of 49
Solution: - Multiply the number by 4: 49×4 = 196
Move decimal one point left = 19.6
Hence, 49 × 40 % = 19.6
Finding
45% of a number
Multiplying a number by 9 is very easy. Leave the
unit digit apart and subtract 1 more than the remaining digits from the
original digit and place it in the LHS, in the RHS place the complement of unit
digit.
Example: - 112 x 9 =?
Solution: - 112 – (11+ 1) / Complement of unit digit
2 = 1008
In order to find 45% of a number follow the steps.
1.
Divide the
number by 2
2.
Multiply the
result obtained by 9
3.
Move the decimal
point one place to left
Example: - Find 45% of 36
Solution: - Divide 36 by 2; 36 ÷ 2 = 18
Multiply it by 9 = 18 ×9 = 162
Move decimal point one place to left = 16.2
Hence, 36 × 45% = 16.2
Example: - Find 45% of 640
Solution: - Divide 640 by 2; 640 ÷ 2 = 320
Multiply it by 9 = 320 ×9 = 2880
Move decimal point one place to left =
288
Hence, 460 × 45% = 288
Finding
50% of a number
It is as simple as asking a Grade 7 student to read
the table of 2. Simply divide the number whose 50% you are intend to find by 2
and you get the answer.
Example: - Find 50% of 630
Solution: - Divide 630 by 2: 630÷2 = 315
Example: - Find 50% of 6850
Solution: - Divide 6850 by 2: 6850÷2 = 3425
Finding
55% of a number
Multiplying a number by 11 is very easy. In
Multiplication chapter I have described a simple rule to multiply any number by
11. Simply put two zeros (along both side one each) with the number and keep
adding from right to left to get the answer.
Example: - 112 ×11 =?
Solution: - 0(112)0 = 0+1 / 1+1 / 1+2 / 2+0 = 1232
In order to find 50% of a number follow the steps.
1.
Divide the
number by 2
2.
Multiply the
result obtained by 11
3.
Move the decimal
point one place to left
Example: - Find 55% of 36
Solution: - Divide 36 by 2; 36 ÷ 2 = 18
Multiply it by 11 = 18 ×11 = 198
Move decimal point one place to left = 19.8
Hence, 36 × 55% = 19.8
Example: - Find 55% of 580
Solution: - Divide 640 by 2; 580 ÷ 2 = 290
Multiply it by 11 = 290 × 11 = 3190
Move decimal point one place to left =
319
Hence, 460 × 55% = 319
Read more on percentage in my book MATHS MADE EASY published by Rupa Publication
Send your comments at
Rajesh Kumar Thakur
rkthakur1974@gmail.com
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