Question

Divide: 127 and 3
How many groups? _
Write the dividend in expanded form.
127 divided by 3
127 = 100 + _ + 7
Regroup the hundreds piece into 10 tens.
The quotient is the size of the groups. There is 1 left over:
42 R_
Check the answer. Multiply the quotient by the divisor and add the remainder.
42
x3
----
126 + 1 = _
Our answer is confirmed.

Answer 1

Let's go through the division step by step as you've outlined:

1. **Division Setup:**
- We need to divide 127 by 3.

2. **Expanded Form:**
- We write 127 in expanded form:
\[
127 = 100 + 20 + 7
\]

3. **Regrouping:**
- We can regroup the hundreds piece (100) into 10 tens, which gives us:
\[
127 = 10 \times 10 + 20 + 7 = 10 \times 10 + 2 \times 10 + 7
\]
- After regrouping the 100 into tens, we have:
\[
127 = 120 + 7
\]

4. **Performing the Division:**
- We will divide 127 by 3:

- Divide 12 (from 120) by 3:
\[
12 \div 3 = 4
\]
- Now, multiply back to find out how many groups of 3 fit into 12:
\[
4 \times 3 = 12
\]

- Subtract to find the remainder:
\[
12 - 12 = 0
\]

- Bring down the next digit (which is 7), making it 07.
- Now divide 7 by 3:
\[
7 \div 3 = 2
\]
- Multiply back to find out how many groups of 3 fit into 7:
\[
2 \times 3 = 6
\]

- Subtract to find the remainder:
\[
7 - 6 = 1
\]

5. **Quotient and Remainder:**
- The quotient from our division is:
\[
42
\]
- And the remainder is:
\[
1
\]
- So, we can write:
\[
127 \div 3 = 42 \text{ R } 1
\]

6. **Check the Answer:**
- To confirm that our answer is correct, we multiply the quotient by the divisor and add the remainder:
\[
42 \times 3 + 1
\]
- First, multiply:
\[
42 \times 3 = 126
\]
- Then, add the remainder:
\[
126 + 1 = 127
\]

Thus, our answer is confirmed. The final result of dividing 127 by 3 is:
\[
42 \text{ R } 1
\]