MATHEMATICS: Shortcuts in Multiplication, Division, Addition & Subtraction - secrets in mental math calculation speed

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By eternaltreasures

There are many useful Math techniques, tricks, and secrets that can be valuable in your day to day work or study. Knowing these shortcuts are key to computation speed and accuracy in your Mental Mathematical Aptitude. This can be useful in applications such as IQ tests, aptitude tests, job application tests, military tests, college entrance tests and so many more uses in the office, workplace, or in your own home.


MULTIPLICATION:


Multiplication using multiples
12 x 15
= 12 x 5 x 3
= 60 x 3
= 180

Multiplication by distribution
12 x 17
= (12 x 10) + (12 x 7) ---> 12 is multiplied to both 10 & 7
= 120 + 84
= 204

Multiplication by "giving and taking"
12 x 47
= 12 x (50 - 3)
= (12 x 50) - (12 x 3)
= 600 - 36
= 564

Multiplication by 5 --> take the half(0.5) then multiply by 10
428 x 5
= (428 x 1/2) x 10 = 428 x 0.5 x 10
= 214 x 10
= 2140

Multiplication by 10 ---> just move the decimal point one place to the right
14 x 10
= 140 ---> added one zero

Multiplication by 50 ---> take the half(0.5) then multiply by 100
18 x 50
= (18/2) x 100 = 18 x 0.5 x 100
= 9 x 100
= 900

Multiplication by 100 ---> move the decimal point two places to the right
42 x 100
= 4200 ---> added two zeroes

Multiplication by 500 ---> take the half(0.5) then multiply by 1000
21 x 500
= 21/2 x 1000
= 10.5 x 1000
= 10500

Multiplication by 25 ---> use the analogy $1 = 4 x 25 cents
25 x 14
= (25 x 10) + (25 x 4) ---> 250 + 100 ---> $2.50 + $1
= 350

Multiplication by 25 ---> divide by 4 then multiply by 100
36 x 25
= (36/4) x 100
= 9 x 100
= 900

Multiplication by 11 if sum of digits is less than 10
72 x 11
= 7_2 ---> the middle term = 7 + 2 = 9
= place the middle term 9 between 7 & 2
= 792

Multiplication by 11 if sum of digits is greater than 10
87 x 11
= 8_7 ---> the middle term = 8 + 7 = 15
because the middle term is greater than 10, use 5 then
add 1 to the first term 8, which leads to the answer of
= 957

Multiplication of 37 by the 3, 6, 9 until 27 series of numbers --> the "triple effect"           
solve 37 x 3               
multiply 7 by 3 = 21, knowing the last digit (1), just combine two more 1's giving the triple digit answer 111           
               
solve 37 x 9               
multiply 7 by 9 = 63, knowing the last digit (3), just combine two more 3's giving the triple digit answer 333           
                   
solve 37 x 21               
multiply 7 by 21 = 147, knowing the last digit (7), just combine two more 7's giving the triple digit answer 777       
                   
Multiplication of the "dozen teens" group of numbers --
(i.e. 12, 13, 14, 15, 16, 17, 18, 19) by ANY of the numbers within the group:
solve 14 x 17               
4 x 7 = 28;  remember 8, carry 2               
14 + 7 = 21               
add 21 to whats is carried (2)               
giving the result 23               
form the answer by combinig 23 to what is remembered (8)               
giving the answer 238   

Multiplication of numbers ending in 5 with difference of 10
45 x 35
first term = [(4 + 1) x 3] = 15; (4 is the first digit of 45 and 3 is the first digit of 35 --> add 1 to the higher first digit which is 4 in this case, then multiply the result by 3, giving 15)
last term = 75
combining the first term and last term,
= 1575

75 x 85
first term = (8 + 1) x 7 = 63
last term = 75
combining first and last terms,
= 6375

15 x 25
= 375

Multiplication of numbers ending in 5 with the same first terms (square of a number)
25 x 25
first term = (2 + 1) x 2 = 6
last term = 25
answer = 625 ---> square of 25

75 x 75
first term = (7 + 1) x 7 = 56
last term = 25
answer = 5625 ---> 75 squared



DIVISION:


Division by parts ---> imagine dividing $874 between two persons
874/2
= 800/2 + 74/2
= 400 + 37
= 437

Division using the factors of the divisor: "double division"
70/14
= (70/7)/2 ---> 7 and 2 are the factors of 14
= 10/2
= 5

Division by using fractions:
132/2
= (100/2 + 32/2) ---> break down into two fractions
= (50 + 16)
= 66

Division by 5 ---> divide by 100 then multiply by 20
1400/5
= (1400/100) x 20
= 14 x 20
= 280

Division by 10 ---> move the decimal point one place to the left
0.5/10
= 0.05 ---> 5% is 50% divided by ten

Division by 50 ---> divide by 100 then multiply by 2
2100/50
= (2100/100) x 2
= 21 x 2
= 42

700/50
= (700/100) x 2
= 7 x 2
= 14

Division by 100 ---> move the decimal point two places to the left
25/100
= 0.25

Division by 500 ---> divide by 100 then multiply by 0.2
17/500
= (17/100) x 0.2
= 0.17 x 0.2
= 0.034

Division by 25 ---> divide by 100 then multiply by 4
500/25
= (500/100) x 4
= 5 x 4
= 20

750/25
= (750/100) x 4
= 7.5 x 2 x 2
= 30



ADDITION:


Addition of numbers close to multiples of ten (e.g. 19, 29, 89, 99 etc.)
116 + 39
= 116 + (40 - 1)
= 116 + 40 - 1 ---> add 40 then subtract 1
= 156 - 1
= 155

116 + 97
= 116 + (100 - 3)
= 116 + 100 - 3 ---> add 100 then subtract 3
= 216 - 3
= 213

Addition of decimals
12.5 + 6.25
= (12 + 0.5) + (6 + 0.25)
= 12 + 6 + 0.5 + 0.25 ---> add the integers then the decimals
= 18 + 0.5 + 0.25
= 18.75


SUBTRACTION:


Subtraction by numbers close to 100, 200, 300, 400, etc.
250 - 96
= 250 - (100 - 4)
= 250 - 100 + 4 ---> subtract 100 then add 4
= 150 + 4
= 154

250 - 196
= 250 - (200 - 4)
= 250 - 200 + 4 ---> subtract 200 then add 4
= 50 + 4
= 54

216 - 61
= 216 - (100 - 39)
= 216 - 100 + 39
= 116 + (40 - 1) ---> now the operation is addition, which is much easier
= 156 - 1
= 155

Subtraction of decimals
47 - 9.9
= 47 - (9 + 0.9) ---> "double subtraction"
= 47 - 9 - 0.9 ---> subtract the integer first then the decimal
= 38 - 0.9
= 37.1

18.3 - 0.8
= 18 + 0.3 - 0.8
= (18 - 0.8) + 0.3 ---> subtract 0.8 from 18 first
= 17.2 + 0.3
= 17.5


WORKING ON PERCENTAGES:


30% of 120
= 10% x 3 x 120 ---> it is much easier working with tens (10%)
= 10% x 120 x 3
= 12 x 3
= 36

five percent of a number: 5%
360 x 5%
= 360 x 10%/2 ---> take the 10% and divide by 2
= 36/2
= 18

360 x 5%
= 360 x 50%/10 ---> take the half(0.5) and divide by 10
= (360/2)/10
= 180/10
= 18

ninety percent of a number: 90%
90% of 700
= (100% - 10%) x 700
= (100% x 700) - (10% x 700) ---> 100% minus 10% of the number
= 700 - 70
= 630

What is 18 as a percentage of 50?
= 18/50
= (18/100) x 2 ---> method: division by 50 (explained above)
= 0.18 x 2
= 0.36
= 36%

What is 132 as a percentage of 200?
= 132/200
= (132/2)/100
= [100/2 + 32/2]/100 ---> solution by "double division"
= (50 + 16)/100
= 66/100
= 0.66
= 66%

What is 270 as a percentage of 300?
= 270/300
= [(270/3)/100] ---> "double division" (using the factors of 300)
= 90/100
= 90%

What is 17 as percentage of 500?
= 17/500
= (17/50)/10
= (17/100) x 2/10 ---> solution using the procedure: division by 50
= (0.17 x 2)/10
= 0.34/10
= 0.034
= 3.4 %

percentages close to 100:
95% of 700
= (100% - 5%) x 700
= (100% x 700) - (5% x 700)
= 700 - (10% x 700/2) -------> 5% is 10%/2
= 700 - 70/2
= 700 - 35
= 665

percentages less than 10 percent:
3% of 70
= (3/100) x 70
= (70/100) x 3 ---> divide by 100 then multiply the percent value
= 0.7 x 3
= 2.1


DECIMALS:


To convert or express percentages as decimals, divide by 100 or simply just move the decimal point by two places to the left of the given number, thus:

1% = 1/100 = 0.01
2% = 2/100 = 0.02 = 1/50
3% = 3/100 = 0.03
4% = 4/100 = 0.04 = 1/25
5% = 5/100 = 0.05 = 1/20
6.25% = 6.25/100 = 0.0625 = 1/16
7% = 7/100 = 0.07
7.5% = 7.5/100 = 0.075
10% = 10/100 = 0.1 = 1/10
12.5% = 12.5/100 = 0.125 = 1/8
20% = 0.2 = 1/5
21% = 0.21
25% = 0.25 = 1/4
30% = 0.3 = 3/10
33.33% = 33.33/100 = 0.3333 = 1/3
37.5% = 0.375 = 3/8
40% = 0.4 = 2/5
50% = 0.5 = 1/2
60% = 0.6 = 3/5
62.5% = 0.625 = 5/8
66.66% = 66.66/100 = 2/3
75% = 0.75 = 3/4
80% = 0.8 = 4/5
87.5% = 0.875 = 7/8
100% = 1
125% = 1.25 = 1 1/4
150% = 1.5 = 1 1/2
200% = 2



FRACTIONS:


What is three quarters of 80?
= 3/4 x 80
= (80/4) x 3 ---> divide by 4 then multiply by 3
= 20 x 3
= 60

How many quarters in two and a half?
2.5/.25
= 10 ---> there are 10 quarters in $2.50


Improper fractions:

3/2 = 1 1/2 = 1.5 = 150%

4/3 = 1 1/3 = 1.3333 = 133.33% ---> useful number for volume of sphere, etc.

9/5 = 1 4/5 = 1.8 = 180% ---> conversion factor for Celsius/Fahrenheit temperatures


V = 4/3 pi * r^3

where:

V = volume of sphere
r = radius of sphere


F = (1.8 C) + 32

where:

F = temperature in Fahrenheit
C = temperature in Celsius

See also:

MATHEMATICS:

IQ TESTS - VOCABULARY APTITUDE:

See also:

MECHANICAL ENGINEERING:

Comments

Niteen 2 weeks ago

thanks for shairing such information. its realy hepls a lot...

suba 3 weeks ago

very useful

Avinash 5 weeks ago

useful information ,it is

mark 7 weeks ago

please include this link in your article

i am sure that this link deserves to be included at the top

http://science-and-mathematics.blogspot.com/2012/0

sushi 2 months ago

its really works guys...........

sachin 3 months ago

it's a good tricks for fresher .

thank u for this

EmperiusIND 3 months ago

Please visit my blog: www.mathshortcuts1.blogspot.com

You have all what you need.

Thats it. :-) :-)

GOVARDHAN REDDY ( MATHEMATICIAN) 3 months ago

ALL IN THE SITES HAVING SAME TYPE OF SHORT CUTS THERE IS NO CHANGE NEW IDEAS MUST TO BE DEVELOPED

THANK U

sharon 9 months ago

i have many more shocuts in multiplication and division

rahul 12 months ago

a b c

* d e f

________

sunita.s 13 months ago

thank you so much for the short cuts but i also need decimal multiplication short cuts like 4.6*5.8

Emperius 14 months ago

For easy math squaring,multiplication,Division,Addition,Subtraction, percentage shortcuts contact me at iforindia123@gmail.com

For example to show one of my methods:

To square a two digit number, say 74

7^2=49

(7*4)2=56

4^2=16

now add the digit other than the ones digit with previous number.

1. 49 cant be added with a previous number.

2. add the 5 of 56 with 49, 49+5=54 then simply attach the ones digit.becomes 546

3. similarly add 1 of 16 with 546 and attach 6.

you get 5476.

this is the square of 74.

i.e. 74^2=5476 :-) :-) :-) :-) :-) :-)

http://mathshortcuts1.blogspot.com/ (Under construction)

Harish Chakrawarthy 14 months ago

For easy math squaring shortcuts and multiplication shortcuts contact me at iforindia123@gmail.com

For example to show one of my methods:

To square a two digit number, say 74

7^2=49

(7*4)2=56

4^2=16

now add the digit other than the ones digit with previous number.

1. 49 cant be added with a previous number.

2. add the 5 of 56 with 49, 49+5=54 then simply attach the ones digit.becomes 546

3. similarly add 1 of 16 with 546 and attach 6.

you get 5476.

this is the square of 74.

i.e. 74^2=5476 :-) :-) :-) :-) :-) :-)

madhu 14 months ago

this is very good to learn maths on net . i am so happy even i can do in office b'coz i dont hav pc at my home.thanks a lot

chinna_sri 15 months ago

it is very use ful to solve every problem

mathematician 19 months ago

what a wonderful website !!!

I hope this will help me in my Mathematics quiz bee , you let me remember everything teached to me by my teachers win or lose THANK YOU !!!!!!!!!!!!!!!!!!

eternaltreasures profile image

eternaltreasures Hub Author 19 months ago

dear Paul

thank you for sharing your website. It sure would be helpful for mental math learners.

paul 19 months ago

try superTmatik Mental Math, a developmental, teaching card game aimed at motivating students to learn and enjoy maths. The product of innovative ingenuity, the superTmatik mental maths game is in essence a key teaching tool to improve calculation skills. It is fully differentiated, catering not only for different age groups, but also different levels of ability (www.mentalmathcompetition.com

ntenda nakafwaya kalenga 21 months ago

this is a very nice site and very helpful to. You just need to make it esier to find and more well known!

eternaltreasures profile image

eternaltreasures Hub Author 22 months ago

to all,

I have added two shortcuts: Multiplication by 37 and Multiplication of the "DOZEN TEENS"

eternaltreasures profile image

eternaltreasures Hub Author 23 months ago

hi tkumah,

thanks for commenting and praising my hub. I will my sure my kids will have fun learning math.

Tkumah profile image

Tkumah 23 months ago

I have used some of the methods naturally since I love math but I could not help but notice how wonderful is this hub. Those are ideas that not only looks good but also work well in real life.

It is too bad that math is such a scary subject to kids while it is in reality fun and play.

eternaltreasures profile image

eternaltreasures Hub Author 23 months ago

hi urs_dipak,

Thanks for your comment. I got the inspiration to compile all these shortcuts because they are very useful in almost every area of technology, science and in various fields of study and profession, even in our daily lives, they have universal and practical applications.

urs_dipak profile image

urs_dipak 23 months ago

Very useful and nice tips. Thanks for those

eternaltreasures profile image

eternaltreasures Hub Author 23 months ago

hi tonysama,

thanks for your comment. As soon as I discover new tricks and secrets, I will share it in this hub.

TonySama profile image

TonySama 23 months ago

This is a good one. I tutor and used many of these to help the kids. However, the 11 one, that's genius that I'd not seen before.

eternaltreasures profile image

eternaltreasures Hub Author 23 months ago

dear dahoglund,

thank you for your comments. I hope this hub can be useful.

dahoglund profile image

dahoglund Level 7 Commenter 23 months ago

When I was a kid we were required to learn the multiplication tables. However, I never did. my brother who was quite smart in stuff like math and later became an engineer taught me several of these techniques. As such I could pass the test and the teachers did not realize that I didn't know the table. However, I have learned to regret the lack of memorization skills.

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