Question

How is the quotient of 704 and 24 determined using an area model?

Answer 1

To determine the quotient of 704 and 24 using an area model, create a rectangle with a length of 704 units and a width of 24 units. The area represents the product of 704 and 24. Divide the area by the width to find the quotient.

Step-by-step explanation:

To determine the quotient of 704 and 24 using an area model, we can create a rectangle with a length of 704 units and a width of 24 units. The area of the rectangle represents the product of 704 and 24. We can then find the quotient by dividing the area of the rectangle by the width of 24 units.

Area = Length × Width

Area = 704 × 24 = 16896

Quotient = Area ÷ Width = 16896 ÷ 24 = 704

This approach, utilizing an area model, provides a visual representation of the division of 704 by 24, where the rectangle's area corresponds to their product. Dividing this area by the width (24 units) effectively yields the quotient, emphasizing a concrete and illustrative method for understanding division through the context of geometric models.

Answer 2

To find the quotient of 704 and 24 using an area model, divide the area represented by 704 into sections that each represent a multiple of 24, and sum the number of these sections.

Step-by-step explanation:

To determine the quotient of 704 and 24 using an area model, you can begin by setting up a rectangular area divided into sections that represent the dividend (704) in terms of the divisor (24). Start by asking how many times 24 can fit into 704. You know that 24 times 10 is 240, which is a part of 704. That gives you a section of the rectangle. You would then subtract 240 from 704 to determine the remaining area you need to cover. This subtraction gives you 464. You would then find out how many times 24 fits into 464. Continuing in this fashion, until you have covered the entire area of 704 with sections representing multiples of 24. By summing the number of 24s used, you arrive at the quotient. In this case, dividing 704 by 24 results in a quotient of 29, with a remainder of 8.