Question

Dividing by Finding Group Size with Zeros in the Dividend
Divide: 1,205 ÷ 3
How many groups? 3
Write the dividend in expanded form.
1205÷____
(1,000 + 200 x 5) ÷ 3
Regroup the thousand block into_____hundreds.
Our quotient is the size of the groups. Each group contains blocks and 1 one’s block,
The quotient is____with a remainder of 2.

Answer 1

To divide \( 1,205 \) by \( 3 \) effectively, we can break down the process step by step.

1. **Expanded Form**: Write the dividend \( 1,205 \) in expanded form.
\[
1205 = 1000 + 200 + 5
\]

2. **Regrouping**: We can regroup the thousands into hundreds:
\[
1000 = 10 \times 100
\]
So, regrouping the thousand block into hundreds results in:
\[
1205 = (10 \times 100) + 200 + 5 = 1200 + 5
\]

Thus, we can also express \( 1205 \) as:
\[
(1000 + 200 + 5) = (10 \text{ hundreds}) + 2 \text{ hundreds} + 5
\]

3. **Division**: Now we divide each block by \( 3 \):
- For \( 10 \) hundreds (from the thousand block):
\[
1000 \div 3 = 333 \text{ (with a remainder of } 1 \text{)}
\]
- For \( 2 \) hundreds:
\[
200 \div 3 = 66 \text{ (with a remainder of } 2 \text{)}
\]
- For the \( 5 \):
\[
5 \div 3 = 1 \text{ (with a remainder of } 2 \text{)}
\]

4. **Adding Quotients Together**:
- From \( 1000 \): \( 333 \)
- From \( 200 \): \( 66 \)
- From \( 5 \): \( 1 \)

Add them together:
\[
333 + 66 + 1 = 400
\]

The complete division can be summarized as:
- The quotient is \( 401 \) (since we accounted for the remainders, we added \( 1 \) to the total groups created).

5. **Final Answer**:
\[
1205 \div 3 = 401 \text{ with a remainder of } 2.
\]

So the final statements can be filled in as follows:
- The expanded form: \( 1205 \div (1000 + 200 + 5) \)
- Regroup the thousand block into **10 hundreds**.
- Our quotient is the size of the groups. Each group contains blocks and **1 one’s block**.
- The quotient is **401** with a remainder of **2**.