Ten of one digit, plus the other
Show on a big screen52 has a tens digit and a ones digit: 5 and 2. A digit is one of 0 to 9. The reverse of 52 is 25: the same digits, written backwards.
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- 52 is 5 tens and 2 ones.
- Reverse the digits: 2 tens and 5 ones. That is 25.
- 52 + 25 = 77.
- 77 = 11 × 7.
The rule
Call the tens digit a and the ones digit b. The tens digit a means a groups of 10, which is 10a. So the number is worth 10a + b. The reverse is 10b + a.
Add them: (10a + b) + (10b + a) collects to 11a + 11b. Here 10a + a = 11a and 10b + b = 11b. Take out the common 11 to get 11(a + b).
The digit sum is a + b, the digits added up.
Rule: For two digits, number plus reverse is 11 times digit sum.
| Number | Reverse | Sum | a + b | 11 × (a + b) |
|---|---|---|---|---|
| 52 | 25 | 77 | 7 | 77 |
| 71 | 17 | 88 | 8 | 88 |
| 63 | 36 | 99 | 9 | 99 |
| 40 | 04 | 44 | 4 | 44 |
40 reversed is 04, which is 4. Here b is 0, and the rule still holds.
Watch out!
10a + b does not mean a times b. Two digits together mean ten of the first, plus the second. 52 is 50 + 2, not 5 × 2.
Try the lab to finish this lesson.