Subtraction

Compensation works with thousands too. Ones: \(2 - 5\) is not possible, add \(10\) ones on top and compensate with \(1\) ten below: \(12 - 5 = 7\). Tens: \(1 - 7 - 1\) is not possible, add \(10\) tens on top, compensate with \(1\) hundred below: \(11 - 7 - 1 = 3\). Hundreds: \(0 - 8 - 1\) is not possible, add \(10\) hundreds on top, compensate with \(1\) thousand below: \(10 - 8 - 1 = 1\). Thousands: \(7 - 4 - 1 = 2\). \(7\,012 - 4\,875 = 2\,137\). Check: \(2\,137 + 4\,875 = 7\,012\).

A zero in the top number is treated like any digit that is too small: \(10\) is added to it, and \(1\) is added to the next digit of the bottom number.

• Ones: \(3 - 8\) is not possible. Add \(10\) ones to the top number, making \(13\) ones, and \(1\) ten to the bottom number: \(13 - 8 = 5\).
• Tens: \(0 - 6 - 1\) is not possible. Add \(10\) tens to the top number, making \(10\) tens, and \(1\) hundred to the bottom number: \(10 - 6 - 1 = 3\).
• Hundreds: \(4 - 5 - 1\) is not possible. Add \(10\) hundreds to the top number, making \(14\) hundreds, and \(1\) thousand to the bottom number: \(14 - 5 - 1 = 8\).
• Thousands: \(0 - 7 - 1\) is not possible. Add \(10\) thousands to the top number, making \(10\) thousands, and \(1\) ten thousand to the bottom number: \(10 - 7 - 1 = 2\).
• Ten thousands: \(6 - 2 - 1 = 3\).

So \(60\,403 - 27\,568 = 32\,835\).
Check with an addition, the result plus the number taken away: \(32\,835 + 27\,568 = 60\,403\), the starting number.