To determine the quotient of 3,419 and 11 using an area model, we can break down 3,419 into parts that are easier to divide by 11.
- We can break down 3,419 into 3,000 + 400 + 19.
- Then, we can divide each part by 11 separately.
Let's proceed with the equations:
- Breaking down 3,419:
\[ 3,419 = 3,000 + 400 + 19 \]
So, we express it as:
\[ 3,419 ÷ 11 = (3,000 ÷ 11) + (400 ÷ 11) + (19 ÷ 11) \]
- Calculating each part:
- \( 3,000 ÷ 11 \approx 272.72 \)
- \( 400 ÷ 11 \approx 36.36 \)
- \( 19 ÷ 11 \approx 1.73 \)
To simplify, we may round off values for practical use:
- \( 3,000 ÷ 11 = 272\)
- \( 400 ÷ 11 = 36\)
- \( 19 ÷ 11 = 1\)
- Now we can finish the equations:
Combining these, we get:
\[ 3,419 ÷ 11 = 272 + 36 + 1 \]
Finally:
\[ 3,419 ÷ 11 = 309 \]
-
Combining everything together:
-
First equation completed:
\[ 3,419 ÷ 11 = (3,000 ÷ 11) + (400 ÷ 11) + (19 ÷ 11) \]
- Filling in the direct calculations:
\[ 3,419 ÷ 11 = 272 + 36 + 1 \]
- The final quotient:
\[ 3,419 ÷ 11 = 309 \]
Putting it all together into the boxes, here is the final result:
- \( 3,000 \)
- \( 400 \)
- \( 19 \)
- \( 272 \)
- \( 36 \)
- \( 1 \)
- \( 309 \)
So:
- 3,419 ÷ 11 = (3,000 ÷ 11) + (400 ÷ 11) + (19 ÷ 11)
- 3,419 ÷ 11 = 272 + 36 + 1
- 3,419 ÷ 11 = 309