## Subtraction with Regrouping

If your friend has 34 marbles and gives you 16 of them, how many is she left with?

To find the answer, you have to subtract 16 from 34. You can use subtraction with regrouping to do so.

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## What is Subtraction with Regrouping?

Let’s understand the method of subtraction with regrouping to find the answer to the previous question.

As we arrange the numbers in a column according to their place value, you can see that 4 is smaller than 6. We can’t subtract 6 from 4. So, what do we do?

This is where the concept of regrouping comes into play. Let’s explore some important terms first.

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## Terms to Know

We use certain terms when subtracting two numbers. They are:

**Minuend**

The number from which we subtract another number.

**Subtrahend**

The number which we subtract from the minuend.

**Difference**

The result we get when we subtract the subtrahend from the minuend.

We write the subtraction formula as:

**Minuend – Subtrahend = Difference**

Let us consider the subtraction equation 13 – 4 = 9. Here, 13 is the minuend, 4 is the subtrahend, and 9 is the difference.

In the vertical method of subtraction or column method:

## Subtraction with Regrouping Steps

We use regrouping in subtraction when one or more digits in the subtrahend are larger than the corresponding digits in the minuend. Let’s see how to do subtraction with regrouping.

To do this, we borrow 1 from the immediate next column on the left and regroup the numbers. It increases the value of the minuend. This enables us to carry out the subtraction.

Let us understand this with the above example of marbles, where we must subtract 16 from 34.

**Step 1:** Place the numbers vertically, aligning the place values, with the minuend at the top and the subtrahend below.

In the ones column, the minuend 4 is smaller than the subtrahend 6. But we cannot subtract 6 from 4. So, we borrow 1 from the tens column and get 14 ones in the ones column. Now, we can easily subtract 6 from 14.

**Step 2: **Next, focus on the tens column. Since we regroup 1 ten as 10 ones into the ones column, the value in the tens place will reduce by 1. This means we decrease 1 from 2. So, we are left with 1 in the tens column. We carry out the subtraction after this regrouping.

## Application of Subtraction with Regrouping in Real Life

Subtraction with regrouping is very useful in our daily life. We often apply this concept to:

- Measure distance
- Measure time
- Deal with money

## Solved Examples

**Example 1: The length of a running track is 195 meters. Mark ran 49 meters. How much distance does he need to cover to complete the track?**

**Solution:** We arrange the numbers vertically.

Here, the minuend 5 in the ones column is smaller than the subtrahend 9. We borrow 1 from the tens column and get 15 ones in the ones column. We subtract 9 from 15 ones and get 6.

Now, we move on to the tens column.

Since we regroup 1 ten as 10 ones into the ones column, the value in the tens place will reduce by 1. This means we decrease 1 from 9 and carry out the subtraction.

Then we move on to the hundreds column, and we get 146 as the answer.

**Example 2: Subtract 158 from 312.**

**Solution:** We arrange the numbers in columns.

Here, the minuend 2 in the ones column is smaller than the subtrahend 8. So, we borrow 1 from the tens column and get 12 ones in the ones column.

Next, we reduce 1 from the tens column. So, 1 – 1 becomes 0. But the subtrahend in the tens column is 5, which is bigger than 0. So, as before, we borrow 1 from the hundreds column, and since 1 hundred = 10 tens, we get 10 in the tens column, and we carry out the subtraction.

Finally, we reduce 1 from the hundreds column and do the subtraction. We get 154 as the answer.

## Practice Problems

## Subtraction with Regrouping

### Cathy has 34 books. She gives 9 books to Juan. How many books are left with Cathy?

Here, we carry out the subtraction using regrouping as follows:

### A zoo reared 83 reptiles. Out of them, 27 reptiles were released in the wild. How many reptiles were left at the zoo?

Here, we carry out the subtraction using regrouping as follows:

### A basket has 270 red and yellow balls. If the number of red balls is 163, how many yellow balls does the basket have?

Here, we carry out the subtraction using regrouping as follows:

## Frequently Asked Questions

**In subtraction regrouping, can we borrow from any column on the left of the minuend?**

When regrouping, we have to borrow from the column on the immediate left.

**Do we have to always arrange the numbers in columns for subtraction with regrouping?**

Yes, we need to arrange the numbers in columns according to the place value of the digits for subtraction with regrouping.

**How can we check the answer of subtraction regrouping?**

We can add the subtrahend and the difference. If the result equals the minuend, then our answer is correct.