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): $$1000÷3=333\text{ (with a remainder of }1\text{)}$$
   • For $2$ hundreds: $$200÷3=66\text{ (with a remainder of }2\text{)}$$
   • For the $5$: $$5÷3=1\text{ (with a remainder of }2\text{)}$$

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: $$1205÷3=401\text{ with a remainder of }2.$$

So the final statements can be filled in as follows:

• The expanded form: $1205÷(1000+200+5)$
• 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.