 Fast multiplication tricks with zero possibility of error always give you an advantage in competitive examinations and to fulfill this purpose here we would learn about some unique Mental math tricks and tips.

## Use of Percentage in Fast Multiplication

A percentage is a number or ratio expressed as a fraction of 100, denoted using the % sign.

Example: 45%=45/100=0.45

For quick multiplication, the concept of percentage is very useful. Here we would study its application in common calculations.

### Fraction Values of Percentage (Multiplication Tricks)

Suppose we have to find the value of 25% of 324.

Here 25%=25/100=1/4     (1/4 is the fraction value of 25%)

So, the required answer=1/4 × 324=81

It means that to find 25% of any value, it should be divided by 4 (multiplied by 1/4)

In other words, we can say 1/4 is the fraction value of 25%

1/100%=25%

Other important fractions:

1/8=12.5%, 2/8=25%, 3/8=37.5%, 4/8=50%

5/8=62.5%, 6/8=75%, 7/8=87.5%, 8/8=100%

1/6=16.67%  then 83.33%=100%-16.67%=1-1/6=5/6

Que 1: Find 178% of 742

Solution:

Que 2: Find the value of 1667×1428×3738

(a) 7354151788

(b)8543714218

(c)8898219288

(d)9163818218

Solution:

1667=16.67×100=16.67% ×100×100=1/10000

1428=14.28×100=14.28% ×100×100=1/10000

=1/1/3738×100000000

=89×100000000

=8900000000 (Approximately)

So, Option (C) is correct.

Que 3: Find the value of 57×78

Solution:

=57%×100×78

=(50%+5%+2%)×78×100

=(1/2+1/20+2/100)×78×100

=(39+3.9+1.56)×100

=44.46×100

=4446

## Product of numbers whose sum of unit digits is equal to 10

Multiplication Tricks for the product of two numbers in a special case.

Conditions (Multiplication Tricks):

1. Only the unit digits of the two numbers should be different and the sum of the unit digits should be equal to 10.
2. Unit digits could be the same also, in the case of 5 and 5 because 5+5=10.

Que 1: Find the value of 36×34.

Step 1: Product of unit digits= 6×4=24 (It should be of 2 digits)

Step 2: n, a number made by the remaining digits

Here n=3

n×(n+1)=3×4=12

Required product of the numbers=1224

Que 2: Find the value of 151×159.

Step 1: Product of unit digits= 1×9=09 (It should be of 2 digits)

Step 2: n, a number made by the remaining digits

Here n=15

n×(n+1)=15×16=(30/2)×16=240

Required product of the numbers=24009

Que 3: Find the value of 145².

145²=145×145

Step 1: 5²=25

Step 2: 14×15=14×(30/2)=210

Required product of the numbers=21025

## The product of mixed fractions whose sum of fractional parts is equal to 1

Conditions (Multiplication Tricks):

1. The sum of fractional parts =1
2. The whole numbers should be the same.

Que 1: Find the value of $17\frac{2}{7}×17\frac{5}{7}$?

Step 1:  Product of fractional parts=

$\frac{2}{7}×\frac{5}{7}=\frac{10}{49}$

Step 2: n, whole number

n×(n+1)=17×18=17×(17+1)=17²+17=289+17=306

Required product =$306\frac{10}{49}$

Que 2: Find the value of $7\frac{5}{9}×7\frac{4}{9}$?

Step 1:  Product of fractional parts=

$\frac{5}{9}×\frac{4}{9}=\frac{20}{81}$

Step 2: n, whole number

n×(n+1)=7×8=56

Required product =$56\frac{20}{81}$

## The square of any number (Multiplication Tricks)

Here we would use a very common formula of the square but in a different way

(a+b)²=a²+2ab+b²

Que 1: Find the value of 43².

Step 1: Break the number into two parts (a & b)

where ‘b’ is the unit digit and ‘a’ is the remaining part.

Step 2: a² / 2ab / b²

=4² / 2×4×3 / 3²

=16 / 24 / 9

=16+2 / 4 / 9

=18 / 4 / 9

=1849

The required result=1849

Que 2: Find the value of 127².

Step 1: Break the number into two parts (a & b)

where ‘b’ is the unit digit and ‘a’ is the remaining part.

Step 2: a² / 2ab / b²

=12² / 2×12×7 / 7²

=144 / 168 / 49

=144 / 168+4=172 / 9

=144 / 172 / 9

=144+17 / 2 / 9

=161 / 2 / 9

The required result=16129

## Multiplication by 11 (Multiplication Tricks)

Que 1: Find the value of 41573×11.

Que 2: Find the value of 47×11.

= 4 / 4+7=11 / 7

=4+1=5 / 1 / 7

=517

## Magical Pyramids (Multiplication Tricks)

• Series of 1 (Multiplication Tricks):

11×11=121

111×111=12321

1111×1111=1234321

11111×11111=123454321

111111×111111=12345654321

…..and so on

• Series of 3 (Multiplication Tricks):

3²=09

33²=1089

333²=110889

3333²=11108889

33333²=1111088889

333333²=111110888889

…..and so on

• Series of 6 (Multiplication Tricks):

6²=36

66²=4356

666²=443556

6666²=44435556

66666²=4444355556

666666²=444443555556

…..and so on

• Series of 9 (Multiplication Tricks):

9²=81

99²=9801

999²=998001

9999²=99980001

99999²=9999800001

999999²=999998000001

…..and so on

Que: Find the value of 44444×55555.

Solution:

=11111×4×11111×5

=11111²×20

=123454321×20

=2469086420

## Difference between Place Value and Face Value

Place Value: It gives the value of a digit based on its position in a number. It changes according to the place of the digit.

Face Value: The actual value of the digit.

Example: Let’s take the number 24578

## Multiplying the numbers close to 100

Case 1: Both the numbers are below 100

Example (1): 89×97 (Multiplication Tricks)

Example (2): 97×98

Example (3): 88×85

Case 2: Both the numbers are above 100

Example (1): 112×109

Case 3: One number is greater and another is lesser than 100

Example (1): 98×107

Example (2): 88×113

Example (3): 98×103

## Multiplying the numbers close to 1000

The method is the same as given above, with a very slight difference

Example: 1012×989

## Multiplying the numbers close to 10000

Example: 10017×9992

700=7×10²

Example: 688×711

### Multiplying the numbers close to 5000

Example: 4992×5003

Note: Division is easy in comparison to multiplication. So, avoid multiplying with more than one digit to reduce the calculation error and time.

$×5=×\frac{10}{2}$

$×25=×\frac{100}{4}$

$×125=×\frac{1000}{8}$

$×625=×\frac{10000}{16}$

$×75=×\frac{300}{4}$

$×15=×\frac{30}{2}$

….and so on

1. ### Difference between factors and multiples.

Factors: The factor of any number can completely divide that number.
Example: Factors of 12 are 1,2,3,4,6,12.
Multiples: A multiple can be obtained by multiplying any number with an integer.
Example: 12× -1= -12, 12× 0= 0, 12× 1= 12, 12× 5= 60 ,etc.

2. ### What is Prime Factorization?

Every number can be expressed in the form of a product of its Prime factors. This way of expression is known as Prime Factorization.
Example: 12=2²×3, 100=2²×5², 3780=2²×3³×5×7, etc.

3. ### What are the rules of multiplication?

Any number multiplied with zero results in always being zero.
The result of the multiplication of two numbers with different signs is always negative.
Negative × Negative= Positive
Positive × Positive= Positive
Negative × Positive= Negative

4. ### What is the relationship between multiplication and addition?

Multiplication is the quick method of repeated addition of any number.
Example: 4×5=20
The sum of fours, five times: 4×5=4+4+4+4+4
The sum of fives, four times: 4×5=5+5+5+5

5. ### Who invented Multiplication?

Multiplication is one of the four elementary arithmetic operations with addition, subtraction, and division.
The ancient Babylonians are considered the inventors of multiplication tables, dating back to 4000 years.

## Quick Multiplication (Quiz)

12 questions with solutions, based on the concept of quick multiplication.