How is the quotient of 556 and 16 determined using an area model?

To use an area model to determine the quotient of 556 and 16, we can break down the dividend (556) into parts that are easy to divide by 16.

First, let's consider how we can split 556. One reasonable way to break it down is:

1. We know that \( 16 \times 34 = 544 \)
2. We can also determine that there's an additional \( 12 \) left over when we subtract \( 544 \) from \( 556 \).

Thus, we can express \( 556 \) as:

\[ 556 = 544 + 12 \]

Now, we divide each part by \( 16 \):

• First part: \( 544 \div 16 = 34 \)
• Remainder part: \( 12 \div 16 = \frac{12}{16} = \frac{3}{4} \)

So, we can express the equation as:

\[ 556 \div 16 = (544 \div 16) + (12 \div 16) \]

This translates into:

\[ 556 \div 16 = 34 + \frac{3}{4} \]

Finally, in simplest form:

\[ 556 \div 16 = 34 \frac{3}{4} \]

So, we can fill in the boxes:

Answer:

• \( 556 \div 16 = (544 \div 16) + (64 \div 16) + (12 \div 16) \) where \( 544 = 34 \cdot 16 \) and \( 12 \) was not taken via multiplication but used as a remainder.
• Thus, the final answer is:

\[ 556 \div 16 = 34 + 4 + \frac{3}{4} \]

So, in the last box, we write \( \frac{3}{4} \).

Therefore:

556 ÷ 16 = (544 ÷ 16) + (64 ÷ 16) + (12 ÷ 16)

Final results:

• \( 556 ÷ 16 = 34 + 4 + \frac{3}{4} \)

Thus, the final answer is:

556 ÷ 16 = \( 34 \frac{3}{4} \)