Question

The area model represents the quotient of 108 ÷ 9. Which equation shown by the area model can be used to find the quotient?

a) (90 - 9) + (18 - 2) = 10 + 9 = 19

b) (90 - 10) + (18 - 2) = 9 + 9 = 18

c) (90 - 1) + (8 - 9) = 9 + 2 = 11

d) (90 - 18) + (18 - 9) = 72 + 9 = 81

Answer 1

The given options for representing the area model of the quotient 108 ÷ 9 are incorrect. The correct equation using the area model should be 90 ÷ 9 + 18 ÷ 9 = 10 + 2 = 12, which results in the quotient of 12.

Step-by-step explanation:

The student has presented a division problem that involves finding an equation to represent the area model of the quotient 108 ÷ 9. Considering the options provided, none of them represent the correct process of division to find the quotient. However, the correct process should be as follows:

First, we must split the dividend, 108, into a sum of numbers that are easily divisible by 9. We can break 108 into 90 and 18, since both 90 and 18 are multiples of 9.

Next, we divide each of these numbers by 9:

• 90 ÷ 9 = 10
• 18 ÷ 9 = 2

Lastly, we add the results to find the total quotient:

10 + 2 = 12

Therefore, the correct equation using the area model to find the quotation of 108 by 9 would be 90 ÷ 9 + 18 ÷ 9 = 10 + 2 = 12. This equation is not listed among the provided options. The student should re-evaluate the problem with this new understanding or look for possible errors in how the question or options were presented.