Same Start Digit, Last Digits Add to 10
This trick works when multiplying two numbers that:
- Have the same number of digits
- Start with the same digit(s)
- And have last digits that add up to 10
Here's the trick:
- Multiply the shared first digit by one more than itself.
- Multiply the last digits of both numbers.
- Stick those two results together!
Let’s look at an example:
83 × 87
(same starting digit: 8, last digits of 3 and 7 add to 10)
(same starting digit: 8, last digits of 3 and 7 add to 10)
8 × 9 = 72
(multiply 8 by one more than itself)
3 × 7 = 21
(multiply the last digits)
(multiply 8 by one more than itself)
3 × 7 = 21
(multiply the last digits)
Put them together: 83 × 87 = 7221
Let’s try one with three digits:
103 × 107
(starts with 10, ends in 3 and 7)
(starts with 10, ends in 3 and 7)
10 × 11 = 110
(multiply 10 by one more than itself)
3 × 7 = 21
(multiply the last digits)
(multiply 10 by one more than itself)
3 × 7 = 21
(multiply the last digits)
Final result: 103 × 107 = 11021
Once you recogize the pattern its quick, give it a try!