Number Story — Predecessor and Successor
Why 20 after 19, 30 after 29…?
15, 16, 17, 18, 19, silence……….the teacher waits for the students to tell 20 but there is a silence!! The teacher helps. Can you relate to this?
Most of us would have heard a class of students practising numbers by singing 0–10, 11–20 etc together in chorus. However, they would be puzzled about why 20 comes after 19 and 30 after 29 and that’s why there’s a pause in the chorus after 19. They would need the help of their teacher to complete the series with 20, 30 and so on.
Here is our attempt to explain the basics of math to remove that confusion.
Why 20 comes after 19, 30 after 29…?
Do you know how numbers got their faces? Yes. You guessed it right!!! It’s from the digits 0 to 9!! Let’s see how.
These are the digits 0–9
0
1
2
3
4
5
6
7
8
9
One day, zero got an idea. It decided to make copies of it and pair up with all digits. Result is
0 → 00
1 → 01
2 → 02
3 → 03
4 → 04
5 → 05
6 → 06
7 → 07
8 → 08
9 → 09
You can see that the first digit “0” is added as a prefix to all the digits.
Now, it’s digit 1’s turn. Digit 1 made copies of it and paired up with all digits.
0 → 00 → 10
1 → 01 → 11
2 → 02 → 12
3 → 03 → 13
4 → 04 → 14
5 → 05 → 15
6 → 06 → 16
7 → 07 → 17
8 → 08 → 18
9 → 09 → 19
You can see that digit “1” is added as a prefix to all digits. Now “2” is ready to make copies of it and get paired. Let’s do that for 2.
0 → 00 → 10 → 20
1 → 01 → 11 → 21
2 → 02 → 12 → 22
3 → 03 → 13 → 23
4 → 04 → 14 → 24
5 → 05 → 15 → 25
6 → 06 → 16 → 26
7 → 07 → 17 → 27
8 → 08 → 18 → 28
9 → 09 → 19 → 29
Now you know why 20 comes after 19? Yes!!
Now, let’s help the digit “3” to make copies and get paired with all digits.
0 → 00 → 10 → 20 → 30
1 → 01 → 11 → 21 → 31
2 → 02 → 12 → 22 → 32
3 → 03 → 13 → 23 → 33
4 → 04 → 14 → 24 → 34
5 → 05 → 15 → 25 → 35
6 → 06 → 16 → 26 → 36
7 → 07 → 17 → 27 → 37
8 → 08 → 18 → 28 → 38
9 → 09 → 19 → 29 → 39
Now you know why 30 is the next number for 29? Yes!!
Ideally, it is good to ask the kids to sing 0 to 9, 11 to 19, 20–29 and so on instead of puzzling them with a different order.
Extension of the concept
Predecessors and successors of a number
Why 499 before 500, 999 before 1000……?
This confusion leads to a situation where the student is unable to find the predecessor and successor of a number. For instance, some children wouldn’t be clear why 499 is the predecessor of 500 or why 500 is the successor of 499. Let’s find the answer with the following example.
Going by the above formation of numbers, we know that 10 would have been prefixed after 9 hence, after 99 we would have 100 and so on.
90–9 with 0 -> 100–10 with 0
91–9 with 1 -> 101–10 with 1
92–9 with 2 -> 102–10 with 2
93–9 with 3 -> 103–10 with 3
94–9 with 4 -> 104–10 with 4
95–9 with 5 -> 105–10 with 5
96–9 with 6 -> 106–10 with 6
97–9 with 7 -> 107–10 with 7
98–9 with 8 -> 108–10 with 8
99–9 with 9 -> 109–10 with 9
Similarly, 49 would have been prefixed with 0 to 9 forming
490 → 49 with 0
491 → 49 with 1
492 → 49 with 2
493 → 49 with 3
494 → 49 with 4
495 → 49 with 5
496 → 49 with 6
497 → 49 with 7
498 → 49 with 8
499 → 49 with 9
Now, can you tell me the number after 49 waiting to create a copy and pair with 0 to 9? Yes!! It’s 50. Hence, 50 pairs with all digits.
500 → 50 with 0
501 → 50 with 1
502 → 50 with 2
503 → 50 with 3
504 → 50 with 4
505 → 50 with 5
506 → 50 with 6
507 → 50 with 7
508 → 50 with 8
509 → 50 with 9
Let us list the above two sets of numbers together.
490 → 49 with 0
491 → 49 with 1
492 → 49 with 2
493 → 49 with 3
494 → 49 with 4
495 → 49 with 5
496 → 49 with 6
497 → 49 with 7
498 → 49 with 8
499 → 49 with 9
500 → 50 with 0
501 → 50 with 1
502 → 50 with 2
503 → 50 with 3
504 → 50 with 4
505 → 50 with 5
506 → 50 with 6
507 → 50 with 7
508 → 50 with 8
509 → 50 with 9
Now, do you understand why 499 is the predecessor of 500 and 500 is the successor of 499? Simple, isn’t it?
