How to borrow three digit subtraction

Welcome! I am excited to help you master 3-digit subtraction. Before we jump into the big numbers, I want to make sure we build a rock-solid foundation so that borrowing feels completely natural.

To help me tailor our session perfectly for you, could you tell me a little bit about your current comfort level with subtraction? Are you already comfortable with place value and basic 2-digit subtraction, or would you like to start from the very basics?

I am comfortable with 2-digit subtraction, let's start there.

It is wonderful that you are already comfortable with 2-digit subtraction, as it gives you a massive head start! Under the hood, subtracting three-digit numbers works exactly the same way, just with one extra column to look after.

The Architecture of a Three-Digit Number

To make sure borrowing feels completely natural rather than like a strange set of rules, we need to think about what our digits actually represent. We use a , which means every step to the left is worth ten times more than the column to its right.

When we look at a number like $352$ , we aren't just looking at a 3, a 5, and a 2. We are looking at a shorthand code for three distinct groups added together:

The Hundreds place: $3$ hundreds ( $300$ )
The Tens place: $5$ tens ( $50$ )
The Ones place: $2$ ones ( $2$ )

A place value mat representing the number 352 using base-ten block models organized into Hundreds, Tens, and Ones columns.

I've started generating an interactive place value mat above to help visualize this. When we 'borrow' during subtraction, all we are doing is breaking apart one of those larger blocks to help out a smaller neighbor that is running short.

Before we look at how that breaking apart works with three digits, let's do a quick check-in. If we break down the number $748$ into its place values, how many tens are in that number?