Multiplication Tricks - Find solution within 20 seconds

Today I am going to share quick multiplication tricks that will help you find the solution within 20 seconds. Must read - 10 Coolest Maths tricks

Multiply by 9,99,999,etc...

56*99=5544

Step 1:Place a zero at the end for each 9 :5600

Step 2 : Subtract the original number from Step 1 like this 5600-56=5544

Multiply by 125

68*125=8500

Step 1 :Place three zeros at the end of the number :68000

Step 2: Divide the number from Step 1  by 8:68000/8=8500

64*125 is the same as :

32*250 is the same as

16*500 is the same as 

8*1000

64*125

Step 1. Each time you just need to pick 125 multiply it by 8 will get 1000

Step 2. Pick 64 and divide it by 8 will get 8

Step 3. Multiply the results with each other 8* 1000 

Hence Solution is 8000

[Hint: Just remember 125*8=1000]

Multiply two digits numbers ending in 1

51*31=1581

Step 1: Multiply the left most digits : 5*3=15

Step 2: Add the left most digits:5+3=8

Step 3: Places the result from Step 2 next to the result from Step 1:158

Step 4 : Places 1 next to the result from  Step 3 : 1581

Multiply numbers between 11 and 19

14*18=252

Step 1: Add the larger  number to the right most digit of the other number:18+4=22

Step 2: Put a 0 at the end of the result from step 1:220

Step 3 :Multiply the right most digits of both original numbers : 8*4=32

Step 4:Add Step 2 and step 3 :220+32=252

Multiply two digit number by 11

53*11=583

Step 1: Add the both digts of the two digit number:5+3=8

Step 2: Place the result in between both digits : 583

59*11=649

Step 1: 5+9=14

Step 2 : Carry the 1 when the result is greater than 9:5+1=6

Step 3: 649

Multiply by 5

 1234 *5 =6170

Step 1 : Divide  the number by 2 :1234/2=617

Step 2: Multiply  the result from Step 1 by 10 : 617*10=6170

Multiply by 25

 18*25=450
Step 1: Divide  the number by 4:18/4
Step 2: Multiply  the number from Step 1 by 100: 4.5 * 100 = 450

Multiply by 9

56*9=504

Step 1: Multiply the number by 10: 56*10=560

Step 2: Subtract the original number from Step 1: 560-56=504

Factorization

By Factoring number,you can break down problems into simpler multiplication tasks.Also,you may be able to apply some techniques you learned.

21*33

step 1 : 21*11*3

Step 2: 231*3

Step 3 :693

67*81

Step 1: 67*9*9

Step 2:603*9=5427

28*125=3500

Step 1: 28*125

Step 2: 28*25*5

Step 3:28*(100/4)*5

Step 4:28/4*100*5

Step 5:7*500=3500

Some Special type

When sum of unit digit is 10 and remaining digit is same.

43×47 = 4 × ( 4+1 ) / 3×7

= 4×⁵/21

= ²⁰/21
Ans = 2021

72×78 = 7×8 / 2×8
= ⁵⁶/16
Ans = 5616

104 × 106 = 10× ( 10+1 ) / 4×6
= 10 × ¹¹/24
= ¹¹⁰/24
Ans = 11024

When sum of ten's digit is 10 and unit digit is same

46 × 66
= ( 4×6 ) +6 / 6×6
= 24 + ⁶/36
= ³⁰/ 36
Ans = 3036

83 × 23
= ( 8×2 ) +3 / 3×3
= ¹⁹/09
Ans = 1909

92 × 12
= ( 9×1 ) + 2/2 × 2
= ¹¹/04
Ans = 1104

When unit digit is 5 in both the numbers and difference between both number is 10.

75 × 65

=  6 × ( 7+1 ) / 75
=  ⁴⁸/75
Ans = 4875

45 × 35
= 3 × ( 4+1 )/75
= 15 /75
Ans = 1575

105 × 95
= 9 × ( 10+1 ) / 75
= 99/75
Ans = 9975

Find the unit digit  of 147¹²⁸ * 138¹⁴⁸ ?

Updated on 12th October 2015

Multiply by 11,111,1111....so on

Ques 1. 111111111 ✘ 111111111 = ?

Sol:
No of digits in multiplier = 9
Write in ascending order from left side like this:
987654321
and now 9-1=8
write it in descending order just after it
12345678
now you will get like this:
12345678987654321
hence
111111111✘111111111 = 12345678987654321

Ques 2. 1111111111 ✘ 1111111111 = ?
Sol:
No of digits in multiplier =10
Write in ascending order from left side like this:
10 9 8 7 6 5 4 3 2 1
and now 10-1=9
write it in descending order just after it
1 2 3 4 5 6 7 8 9
and after it just add the carry
1 2 3 4 5 6 7 8/ 9/ 10 9 8 7 6 5 4 3 2 1
                  8+1/   9+1 / 0
1 2 3 4 5 6 7 9 0 0 9 8 7 6 5 4 3 2 1
now you will get like this:
1234567900987654321
hence
1111111111✘1111111111 = 1234567900987654321

Ques 3. 1111111✘2222222 = ?
Sol:
No of digit in the multiplier is 7 then let n=7;
Now Just multiply the digit 2 from 1 to 7 time & arrange them from extreme left to right in ascending order,you will get like this:
14 12 10 8 6 4 2
and now just subtract one from n.like this n=7,so n-1=6.
Multiply the digit 2 from 1 to 6 time & arrange them from just right after it,you will get like this:
2 4 6 8 10 12
Now placing both outcome like this & add the carry
2 4 6 8 10 12 14 12 10 8 6 4 2
        8+1/0+1/2+1/4+1/2+1
You will get the answer:
2 4 6 9 1 3 5 3 0 8 6 4 2

Ques 4. 1111111✘5555555 = ?
Sol:
No of digit = 7
Now Just multiply the digit 5 from 1 to 7 time & arrange them from extreme left to right in ascending order,you will get like this:
35 30 25 20 15 10 5
Just right after it perform same action but in descending order & till 6 times only.like this:
5 10 15 20 25 30
Now placing together ,just add the carry
5 10 15 20 25 30 35 30 25 20 15 10 5
6 1 7 2 8 3 8 2 7 1 6 0 5
1111111✘5555555=6172838271605