Quick Maths Trick for Times Tables of 55, 555, 5555
Introduction – A Fast Way to Write Times Tables of 5-Based Numbers
Writing multiplication tables for numbers like 55, 555, 5555, 55555, or 555555 may look time-consuming at first. But with this quick mental math trick, you can write down their entire times table easily and systematically—without long multiplication.
This trick works for any number made only of the digit 5 and helps you see the pattern instantly.
There are two cases to understand:
- a simple scenario, and
- a slightly complex scenario.
Once you understand both, writing these times tables becomes almost mechanical.
How the Trick Works – The Simple Scenario
Let's learn this simple scenario with this problem:
55555 7 = 388885
To apply the trick, extract three pieces of information from the problem.
1. Find the Product with 5
Multiply the multiplier (7) of the problem by 5 to get the Product. 75 = 35 is the Product here.
2. The Number of 5s minus 1
The number 55555 has 5 fives. We'll need 5 - 1 = 4 blank spaces.
3. Find the Sum of the Product's Digits
3 + 5 = 8
Since this sum is a single digit, this is a simple scenario.
Apply The Trick
Place the two digits of the Product (35) at extreme ends and add 4 blank spaces in between.
Fill each blank with the Sum (8).
388885 is the final answer.
How the Trick Works – The Complex Scenario
Now let's look at a complex case with this problem, where carrying is required.
55555 19 = 1055545
To apply the trick, extract three pieces of information from the problem.
1. Find the Product with 5
Multiply the multiplier (19) of the problem by 5 to get the Product.
195 = 95 is the Product here.
2. The Number of 5s minus 1
The number 55555 has 5 fives, so we again insert: 5 - 1 = 4 blank spaces.
3. The Sum from the Product
9 + 5 = 14
This is a two-digit sum, so the problem becomes a complex scenario.
Apply the Trick (Right-to-Left Logic)
Place the two digits of the Product (95) at extreme ends and add 4 blank spaces in between.
Imagine the Sum (14) is placed in each blank. Start filling blanks from right to left:
- Write the unit digit of
14(which is4). - Carry the tens digit (
1) to the next left blank. - Repeat this process across all blanks.
Note the logic here works from right to left.
1055545 is the final answer. Once you fully understood the trick, you can simply write down the answer directly.
Complete Times Table Using the Trick
No. of Blanks = No. of 5s in 5555 minus 1 = 3
5555 1 = 5555
5555 2 = 11110
The Product: 25 = 10
The Sum: 1+0 = 1
The blanks: 3
5555 3 = 16665
The Product: 35 = 15
The Sum: 1+5 = 6
The blanks: 3
5555 4 = 22220
The Product: 45 = 20
The Sum: 2+0 = 2
The blanks: 3
5555 5 = 27775
The Product: 55 = 25
The Sum: 2+5 = 7
The blanks: 3
5555 6 = 33330
The Product: 65 = 30
The Sum: 3+0 = 3
The blanks: 3
5555 7 = 38885
The Product: 75 = 35
The Sum: 3+5 = 8
The blanks: 3
5555 8 = 44440
The Product: 85 = 40
The Sum: 4+0 = 4
The blanks: 3
5555 9 = 49995
The Product: 95 = 45
The Sum: 4+5 = 9
The blanks: 3
5555 10 = 55550
5555 11 = 61105
The Product: 115 = 55
The Sum: 5+5 = 10
The blanks: 3
5555 12 = 66660
The Product: 125 = 60
The Sum: 6+0 = 6
The blanks: 3
5555 13 = 72215
The Product: 135 = 65
The Sum: 6+5 = 11
The blanks: 3
5555 14 = 77770
The Product: 145 = 70
The Sum: 7+0 = 7
The blanks: 3
5555 15 = 83325
The Product: 155 = 75
The Sum: 7+5 = 12
The blanks: 3
5555 16 = 88880
The Product: 165 = 80
The Sum: 8+0 = 8
The blanks: 3
5555 17 = 94435
The Product: 175 = 85
The Sum: 8+5 = 13
The blanks: 3
5555 18 = 99990
The Product: 185 = 90
The Sum: 9+0 = 9
The blanks: 3
5555 19 = 105545
The Product: 195 = 95
The Sum: 9+5 = 14
The blanks: 3
5555 20 = 111100
Works fine with Higher Multipliers
This trick is not limited to small numbers or times tables up to 20. It works just as effectively for larger Multiplicands and higher Multipliers.
55555555 7 = 388888885
The Product: 75 = 35
The Sum: 3+5 = 8
The blanks: 7
555555 37 = 20555535
The Product: 375 = 185
The Sum: 18+5 = 23
The blanks: 5
55555 24 = 1333320
The Product: 245 = 120
The Sum: 12+0 = 12
The blanks: 4
555 63 = 34965
The Product: 635 = 315
The Sum: 31+5 = 36
The blanks: 2
Each example follows the same three-step structure, proving that the method is scalable, consistent, and dependable.