Let’s go through the division step-by-step.
-
Written Problem:
- We need to divide: 1,205 ÷ 3
-
How many groups?:
- There are 3 groups.
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Write the dividend in expanded form:
- The dividend can be expressed as: \[ 1,205 = 1,000 + 200 + 5. \] So we can write the division as: \[ 1,205 ÷ 3 = (1,000 + 200 + 5) ÷ 3. \]
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Regroup the thousand block:
- We can regroup the 1,000 into 10 hundreds. Hence, we have: \[ (10,00 + 200 + 5) ÷ 3 = (10 + 2) hundreds + 5 ÷ 3 = 12 hundreds + 5. \]
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Finding the size of the groups:
- Now we can divide each part by 3:
- 1,000 becomes 10 hundreds:
\[
10 ÷ 3 = 3 \text{ (each group gets 3 hundreds)}
\]
- Remainder = 1 hundred
- 200 becomes: \[ 2 ÷ 3 = 0 \text{ (each group gets 0 hundreds)} \]
- 5 becomes:
\[
5 ÷ 3 = 1 \text{ (each group gets 1 ones)}
\]
- Remainder = 2 (because 5 - 3 = 2)
- 1,000 becomes 10 hundreds:
\[
10 ÷ 3 = 3 \text{ (each group gets 3 hundreds)}
\]
- Now we can divide each part by 3:
Now putting this together:
- Each group contains 4 hundred blocks (3 hundreds from the thousands and 0 from the two hundreds) and 1 ones block, with a remainder of 2.
The quotient is: \[ \text{Quotient} = 401\text{ R }2. \]
- Check the calculation:
- To check our work: \[ 401 \times 3 = 1,203 \]
- Then add the remainder: \[ 1,203 + 2 = 1,205. \]
So the final result is: \[ \text{Quotient is } 401 \text{ R } 2. \] This confirms our division is correct.
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