Which method identifies a transposition error in columnar calculations?

Which method identifies a transposition error in columnar calculations?

• A. The decimal point moved in a slide error
• B. Take the difference between two columns and divide by 9
• C. Two numbers were reversed in a column
• D. A debit and credit were posted to the wrong accounts

Answer: (B)

When checking columnar calculations, a transposition error—swapping two adjacent digits within a number—can be detected with a 9-divisibility check. The reason is that swapping digits a and b changes the value from 10a + b to 10b + a, a difference of 9(a − b). So the difference between the sums of two columns, if a transposition occurred, will be a multiple of 9. Dividing that difference by 9 should yield an integer, highlighting that a digit swap happened. For example, swapping 63 to 36 changes the totals by 27, and 27 divided by 9 equals 3, the (a − b) value. This method specifically targets the pattern produced by transpositions, unlike slide errors or posting mistakes, which don’t produce the same 9-based signal.

When checking columnar calculations, a transposition error—swapping two adjacent digits within a number—can be detected with a 9-divisibility check. The reason is that swapping digits a and b changes the value from 10a + b to 10b + a, a difference of 9(a − b). So the difference between the sums of two columns, if a transposition occurred, will be a multiple of 9. Dividing that difference by 9 should yield an integer, highlighting that a digit swap happened. For example, swapping 63 to 36 changes the totals by 27, and 27 divided by 9 equals 3, the (a − b) value. This method specifically targets the pattern produced by transpositions, unlike slide errors or posting mistakes, which don’t produce the same 9-based signal.