4 Digit Subtraction with Regrouping

Instructor: T.J. Hoogsteen

T.J. is currently a grade 5 teacher and Vice-Principal. He has a master's degree in Educational Administration and is working toward an Ed.D. in Educational Leadership.

This lesson will cover 4 digit subtraction. We'll talk about the step by step process for solving these types of problems, including how you can use regrouping to help.

Cleaning by Subtraction

Ever since the creation of digital music devices, people have faced the dilemma of limited storage space for their favorite tunes. The other day I ran into the very same problem. I went to put new music onto my device and I got the error message I was dreading the most: not enough storage. It turns out, I had 4,865 songs and to get new music on I had to get rid of some. So I went through my music and decided what songs were must-keeps and which I could get rid of. After what felt like forever, I had deleted 3,956 songs worth of unnecessary music. I was left wondering how many I had left, so it was time to do some math.

To figure out how many songs were left on my device, I had to complete a four digit subtraction equation. It looked like this:

Example 1

Four Digit Subtraction

A question like this may look scary, like a hungry jungle cat looking for food. But the steps are really just like doing 2 digit or 3 digit subtraction, so if you follow them the problem becomes a whole lot less scary, like a regular house cat. When beginning to work on any subtraction equation, it is a good idea to start in the far right column of digits, which is called the ones column.

Step 1

But after looking more closely at the two numbers, I realized that 6 is bigger than 5 and I couldn't subtract 6 from 5, so I was going to have to regroup, or borrow from the column to the left. In subtraction, if the digit on the bottom is greater than the one on top, regrouping is necessary. After borrowing a ten, I was left with a 5 in the tens column, but I could now subtract because now I had 15-6 in that column.

After subtracting the first two digits this is what I had:


Step 2


When done subtracting the digits in the ones columns, the next step is to move left to the tens column and subtract those two digits.


Step 3


I could subtract 5 from 5 so I didn't need to regroup, and I had this so far:


Step 4


My next step was to keep moving left to the hundreds column and subtract those two digits.


Step 5


Again, the digit in the top row was smaller than the one in the bottom row so I needed to regroup. I borrowed from the column to the left and I was left with 18-9.


Step 6


I subtracted and got this:


Step 7


Finally, I was down to the last column to subtract, the thousands.


When I subtracted, this was my answer.


Step 8


I had 909 songs left. That's still a lot of music, but now I had room to add more, which is exactly what I was going to do.


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