About

Subtraction with regrouping (often called "borrowing") is one of the first major hurdles in arithmetic. When a digit in the bottom row is larger than the digit above it, you must borrow from the neighbor to the left. This tool is designed to make that invisible process visible.

Using a color-coded system, this calculator strikes through modified numbers and shows the temporary values above the columns. This visual reinforcement helps build a strong mental model of base-10 decomposition. It is particularly useful for checking homework or understanding why a specific subtraction yields a certain result.

Formulas

For each column i, if the digit A_i is less than B_i, we perform the operation:

A_i ← A_i + 10

And simultaneously decrement the next higher place value:

A_i+1 ← A_i+1 − 1

Reference Data

Term	Definition	Role
Minuend	The number being subtracted from (A)	Top Row
Subtrahend	The number to be subtracted (B)	Bottom Row
Difference	The result (D)	A − B = D
Borrow	Taking 10 from higher place value	1 ten → 10 ones

Frequently Asked Questions

Borrowing from zero requires a chain reaction. You must travel left to find the first non-zero digit, decrement it, and then propagate the '9s' back to the column that needed the value originally. Our tool visualizes this 'chain borrowing' clearly.

In basic column subtraction, the minuend (top) must be larger than the subtrahend (bottom) to avoid negative results. This tool focuses on the standard algorithm for positive integers. For negative results, one typically swaps the numbers, subtracts, and adds a negative sign.