Sure! Let's break down the division of [tex]\(7,914 \div 6\)[/tex] using an area model.
1. Divide: We begin by considering how many times 6 can fit into 7,914.
2. Estimate: Estimate the highest value 6 fits into.
3. Break it Down: Decompose 7,914 to simplify the division step by step.
4. Calculate Quotient and Remainder: Combine these steps for the final division.
We'll break down 7,914 into manageable parts that can be easily divided by 6.
### Step 1: Decompose the Number
We can decompose 7,914 into parts that are easily divisible by 6.
7,914 can be written as:
- 6 fits into 6,000 (since 6,000 is a multiple of 6)
- The remainder is 1,914
Next, 1,914 can be written as:
- 1,914 can be broken into 1,200 + 600 + 114 (all multiples of 6)
Thus, [tex]\(7,914 = 6,000 + 1,200 + 600 + 114\)[/tex].
### Step 2: Calculate the Quotient for Each Part
1. For 6,000:
[tex]\[
6,000 \div 6 = 1,000
\][/tex]
2. For 1,200:
[tex]\[
1,200 \div 6 = 200
\][/tex]
3. For 600:
[tex]\[
600 \div 6 = 100
\][/tex]
4. For 114:
[tex]\[
114 \div 6 = 19
\][/tex]
### Step 3: Add the Quotients Together
Summing all the quotients:
[tex]\[
1,000 + 200 + 100 + 19 = 1,319
\][/tex]
### Step 4: Verify With Remainder
No remaining parts were left since all parts were cleanly divisible by 6, thus the remainder is:
[tex]\[
0
\][/tex]
### Conclusion
The complete division [tex]\(7,914 \div 6\)[/tex] yields a quotient of 1,319 and a remainder of 0. Thus, the final answer is:
[tex]\[
\boxed{1,319 \text{ with a remainder of } 0}
\][/tex]
