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:

  1. Multiply the shared first digit by one more than itself.
  2. Multiply the last digits of both numbers.
  3. 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)
8 × 9 = 72
(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)
10 × 11 = 110
(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!