Regrouping Hundreds, Tens, and Ones

In math, numbers are grouped into hundreds, tens, and ones. But what happens when you have too many ones or too many tens? You regroup! Regrouping (sometimes called trading) is the secret trick you use when carrying in addition or borrowing in subtraction.

The Magic Rule of 10

Our number system is based on the number 10. The most important rule to remember is:

• $10$ ones = $1$ ten
• $10$ tens = $1$ hundred

Whenever you have $10$ or more in any place value, you can bundle them up and trade them for the next biggest size!

Regrouping Ones into Tens

Let's look at an example: $3$ hundreds, $5$ tens, and $12$ ones.

We cannot have $12$ ones in the ones place! Since $12$ is greater than $10$, we need to regroup.

1. Take $10$ of those ones and trade them for $1$ ten.
2. You are left with $2$ ones.
3. Add the new ten to the $5$ tens you already had: $5 + 1 = 6$ tens.

Answer: $3$ hundreds, $6$ tens, $2$ ones (which is the number $362$).

Regrouping Tens into Hundreds

What if you have too many tens? Let's try: $2$ hundreds, $14$ tens.

We cannot keep $14$ tens in the tens place.

1. Take $10$ of those tens and trade them for $1$ hundred.
2. You are left with $4$ tens.
3. Add the new hundred to the $2$ hundreds you already had: $2 + 1 = 3$ hundreds.

Answer: $3$ hundreds, $4$ tens, $0$ ones (which is the number $340$).

Making Numbers in Different Ways

Because we can trade back and forth, the same number can be written in many different ways. Let's look at the number $243$.

• Standard way: $2$ hundreds, $4$ tens, $3$ ones
• Trade $1$ ten for $10$ ones: $2$ hundreds, $3$ tens, $13$ ones
• Trade $1$ hundred for $10$ tens: $1$ hundred, $14$ tens, $3$ ones

Understanding how to break apart and build numbers like this makes adding and subtracting big numbers a breeze!