What is regrouping in mathematics?
Regrouping is done by creating groups of tens during operations like subtraction and addition. Regrouping involves reorganizing numbers into groups by place value to make it easier to carry out operations.
This process is called regrouping because you rearrange numbers into place values to carry out the operation. Regrouping is a great way to make more significant calculations easier, especially for children. When you’re using regrouping with subtraction, it can also be known as ‘borrowing.’
This helpful method is taught in schools to make addition and subtraction easier for students. If you’re unsure how it’ll work and if it’ll be as easy as it sounds, don’t worry; we’ll take you through the process.
How does regrouping work?
Regrouping may sound complicated when it’s explained, but seeing it in action will show you that it’s not as hard as it sounds. So here are our guides on how to regroup with addition and subtraction.
Regrouping with addition:
- First, we need a problem that we want to solve. Let’s say we want to add 18 and 12, which equals 30.
- When regrouping with addition, it’s best to visualize your problem as a grid. Take a look below for an example:
- The first addition we’d make in this situation would be to add together 2 and 8, which equals 10. But there’s no spot to write ten on the bottom row. So, in this case, we need to use regrouping. To do this, we take the 0 from the ten and place it into the bottom row, then we take the one and put it above our ten’s column. Here’s an updated grid below:
- Now, we need to add up the ten’s columns. In this case, we have three 1s to add together; this brings us to the correct answer to the solution, which is 30.
- But, sometimes, you’re not just using ten-digit numbers. You might need to add up some triple-digit numbers. The process is the same, but you may have to carry over more 1s. Take a look at the example below:
- So, in this case, we need to add 7 and 9, which equals 16. Place the 6 in the bottom and regroup the one above the 3; this now means that our second column becomes 1 + 3 + 6 = 10. We do the same thing again, the 0 from the ten goes to the bottom, and the one goes above the first column; this means our first column is 1 + 1 + 1 = 3. There you have it; our big number problem was solved quickly.
Regrouping with subtraction:
- First, we need to decide what our problem will be. Let’s say we want to solve 33 minus 19, which equals 14. Next, we need to put our numbers into a grid again; look below for an example.
- We can start regrouping now that we have our grid setup. When it comes to subtraction, the process is a little different from addition. We need to ‘borrow’ a ten from the first column, so we take a ten from the 30; this makes our grid look like this:
- Next, we do the calculations. 13 minus 9 equals 4. For the first column, we do 2 – 1 = 1. That leaves us with our answer of 14.
Top of Form
To give you some practice, here are some questions for you to try out with the regrouping method. We’ll put the answers further down the page so you can check them later. See how many you can do and use the guides to help you if you get stuck. Good luck!
- 19 + 23
- 45 + 22
- 56 + 18
- 103 + 219
- 219 + 327
- 33 – 14
- 45 – 27
- 62 – 29
- 93 – 77
- 86 – 37
When is regrouping used in real life?
Regrouping is used, in our lives, whenever people need to use addition and subtraction. You might see this when you’re around the house, doing chores, or organizing your bedroom. You’ll see this when you’re handling money at the shops or buying things online. Adults use addition and subtraction all the time when they’re at work.
Don’t worry if you have to use regrouping at any point; it’s a great and easy method. Suppose you have to pause and get a pen and paper to work out excellent math. Not everyone is a maths whiz and can solve problems in their head. Sometimes you have to write things down to work them out; that’s completely normal. The more you practice this method, the more you’ll start to be able to work out solutions in your head.
Practice question answers
Here are the answers to the questions we gave to you earlier. How many did you get right?
- 19 + 23 = 42
- 45 + 22 = 67
- 56 + 18 = 74
- 103 + 219 = 322
- 219 + 327 = 546
- 33 – 14 = 19
- 45 – 27 = 18
- 62 – 29 = 33
- 93 – 77 = 16
- 86 – 37 = 49