Final answer:
I disagree with Marsha because in long division, the first partial quotient is determined by how many times the divisor can be multiplied without exceeding the first digits of the dividend. Marsha's suggested partial quotient 10 multiplied by 9 gives 90, which is greater than the first two digits, 26, of 261, indicating an incorrect method.
Step-by-step explanation:
I disagree with Marsha's assertion that she can use 10 as the first three partial quotients when finding the division of 261 by 9 (261 ÷ 9). In the process of long division, partial quotients are the results obtained at each step of dividing the dividend by the divisor, before reaching the final quotient or remainder. For the division 261 by 9, the first partial quotient should be the largest number that when multiplied by 9 results in a product that is less than or equal to 261 without exceeding it. The correct first partial quotient should be 2 because 2 times 9 equals 18, which is the highest product of 9 that doesn't exceed the first two digits, 26, of the dividend 261. Following this, we subtract 18 from 26, bring down the next digit, and the process continues until we get the final quotient. Using 10 as a partial quotient would multiply to give 90, which is not only larger than 26, but also doesn't align with the correct steps of long division.