Multiplication Tricks - less than 25 seconds
We are showing some quick multiplication tricks that will help you find the solution within 20 seconds.
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 147^128 * 138^148 ?
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
Multiplication tricks for large numbers
long digit multiplication
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
We are showing some quick multiplication tricks that will help you find the solution within 20 seconds.
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
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
Multiplication tricks for large numbers
long digit multiplication
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
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