Dividing by Finding Group Size with Zeros in the Dividend

Question

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.