Question

1. use basic facts to find the following quotients

5,400 ÷ 9 =
640 ÷ 8 =

1. solve using partial quotient and check with area model

4,421 ÷ 6 =

Explanation:

Part 1: Find the Quotients

For \( 5400 \div 9 \):

Step 1: Recall basic division fact

We know that \( 54 \div 9 = 6 \).

Step 2: Adjust for place value

Since \( 5400 \) is \( 54 \times 100 \), we have \( 5400 \div 9 = (54 \div 9) \times 100 = 6 \times 100 = 600 \).

For \( 640 \div 8 \):

Step 1: Recall basic division fact

We know that \( 64 \div 8 = 8 \).

Step 2: Adjust for place value

Since \( 640 \) is \( 64 \times 10 \), we have \( 640 \div 8 = (64 \div 8) \times 10 = 8 \times 10 = 80 \).

Part 2: Solve \( 4421 \div 6 \) Using Partial Quotient and Check with Area Model

Partial Quotient Method:

Step 1: Subtract multiples of 6 from 4421

• \( 6 \times 700 = 4200 \), so \( 4421 - 4200 = 221 \).
• \( 6 \times 30 = 180 \), so \( 221 - 180 = 41 \).
• \( 6 \times 6 = 36 \), so \( 41 - 36 = 5 \).

Step 2: Sum the partial quotients

Add the multiples: \( 700 + 30 + 6 = 736 \), with a remainder of \( 5 \). Thus, \( 4421 \div 6 = 736 \text{ R } 5 \) (or \( 736 + \frac{5}{6} \)).

Area Model Check:

The area model represents \( 4421 \) as a rectangle with one side \( 6 \). We divide the rectangle into parts:

• A rectangle with area \( 6 \times 700 = 4200 \).
• A rectangle with area \( 6 \times 30 = 180 \).
• A rectangle with area \( 6 \times 6 = 36 \).
• A remaining area of \( 5 \) (the remainder).

Summing the lengths of the sides (quotients) gives \( 700 + 30 + 6 = 736 \), matching the partial quotient result.

Answer:

s:

1. \( 5400 \div 9 = \boldsymbol{600} \); \( 640 \div 8 = \boldsymbol{80} \)
2. \( 4421 \div 6 = \boldsymbol{736 \text{ R } 5} \) (or \( \boldsymbol{736 \frac{5}{6}} \))