# Division With Area Models ## Section A: Multiple Choice Questions
Q1: A rectangle has an area of 48 square units and a width of 6 units. What is the length of the rectangle? (a) 6 units (b) 8 units (c) 42 units (d) 54 units
Solution:
Ans: (b) Explanation: To find the length, we use the area model where \(\text{Area} = \text{length} \times \text{width}\). We divide the area by the width: \(48 \div 6 = 8\) units. The length is 8 units.
Q2: An area model shows a rectangle divided into 3 rows and 4 columns of equal squares. If the total area is 36 square units, what is the area of each small square? (a) 2 square units (b) 3 square units (c) 4 square units (d) 12 square units
Solution:
Ans: (b) Explanation: The rectangle has \(3 \times 4 = 12\) small squares. To find the area of each square, divide the total area by the number of squares: \(36 \div 12 = 3\) square units.
Q3: Using an area model, 63 ÷ 9 can be shown as a rectangle. Which dimensions represent this division? (a) Length = 7, Width = 9 (b) Length = 9, Width = 6 (c) Length = 63, Width = 1 (d) Length = 7, Width = 8
Solution:
Ans: (a) Explanation: In an area model for division, \(63 \div 9\) asks "what times 9 equals 63?" The answer is 7. So the rectangle has length = 7 and width = 9, giving area = 63 square units.
Q4: A rectangle is divided into 10 columns. If the total area is 80 square units, how many rows does the rectangle have? (a) 7 rows (b) 8 rows (c) 9 rows (d) 10 rows
Solution:
Ans: (b) Explanation: The number of rows can be found by dividing the total area by the number of columns: \(80 \div 10 = 8\) rows. This represents the quotient in the division.
Q5: An area model for 56 ÷ 7 shows a rectangle. What is the quotient represented by the other dimension? (a) 6 (b) 7 (c) 8 (d) 9
Solution:
Ans: (c) Explanation: The quotient of \(56 \div 7\) is found by asking "7 times what equals 56?" Since \(7 \times 8 = 56\), the quotient is 8.
Q6: A rectangular area model has a total area of 72 square units and is divided into 8 equal columns. What is the width of each column? (a) 8 units (b) 9 units (c) 10 units (d) 64 units
Solution:
Ans: (b) Explanation: To find the width of each column, divide the total area by the number of columns: \(72 \div 8 = 9\) units. Each column is 9 units wide.
Q7: An area model for division shows a rectangle with area 45 square units and width 5 units. Which multiplication fact helps you find the length? (a) \(5 \times 8 = 40\) (b) \(5 \times 9 = 45\) (c) \(5 \times 10 = 50\) (d) \(5 \times 7 = 35\)
Solution:
Ans: (b) Explanation: We need to find what number times 5 equals 45. The multiplication fact \(5 \times 9 = 45\) shows that the length is 9 units. Division and multiplication are inverse operations.
Q8: A rectangle has an area of 96 square units and length of 12 units. Using the area model, what is the width? (a) 6 units (b) 7 units (c) 8 units (d) 9 units
Solution:
Ans: (c) Explanation: Using the area model, we divide the area by the length: \(96 \div 12 = 8\) units. The width is 8 units.
## Section B: Fill in the Blanks Q9: In an area model for division, the area represents the __________, and one side represents the divisor.
Solution:
Ans: dividend Explanation: The dividend is the number being divided, which is represented by the total area of the rectangle in an area model.
Q10: When using an area model to solve 84 ÷ 7, the quotient is represented by the __________ dimension of the rectangle.
Solution:
Ans: other (or unknown or missing) Explanation: In an area model, one dimension is the divisor (7), and the other dimension represents the quotient (12 in this case).
Q11: A rectangle with area 54 square units and width 6 units has a length of __________ units.
Solution:
Ans: 9 Explanation: Using division: \(54 \div 6 = 9\) units. The length of the rectangle is 9 units.
Q12: The area model connects division to __________, showing that they are inverse operations.
Solution:
Ans: multiplication Explanation: The area model demonstrates that division and multiplication are inverse operations because area = length × width, and we can use division to find an unknown dimension.
Q13: In the division problem 72 ÷ 9 = 8, the number 9 is called the __________.
Solution:
Ans: divisor Explanation: The divisor is the number by which we divide. In this problem, we divide 72 by 9.
Q14: If a rectangle is divided into 7 equal rows with total area 91 square units, each row has an area of __________ square units.
Solution:
Ans: 13 Explanation: Dividing the total area by the number of rows: \(91 \div 7 = 13\) square units per row.
## Section C: Word Problems Q15: Mrs. Johnson has 64 square tiles to arrange in a rectangular pattern. She wants to make 8 equal rows. How many tiles will be in each row? Use an area model to explain your answer.
Solution:
Ans: Step 1: The total area is 64 square tiles. Step 2: The number of rows is 8. Step 3: Divide: \(64 \div 8 = 8\) tiles per row. Final Answer: 8 tiles in each row
Q16: A farmer plants vegetables in a rectangular garden with an area of 96 square feet. The width of the garden is 8 feet. What is the length of the garden?
Q20: Sarah uses 60 square inch tiles to cover a rectangular table. She arranges them in 5 equal columns. If she wants to know how wide each column is, what division problem should she solve and what is the answer?
Solution:
Ans: Step 1: Total tiles = 60 square inches Step 2: Number of columns = 5 Step 3: Division problem: \(60 \div 5\) Step 4: \(60 \div 5 = 12\) square inches Final Answer: The division problem is \(60 \div 5\), and the width of each column is 12 square inches
The document Worksheet (with Solutions): Division With Area Models is a part of the Grade 4 Course Math Grade 4.
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