Question

what was noahs mistake? noah forgot to write a 0 in the ones place. the quotient has 1 hundred and 4 tens, so the quotient is 140. noah didnt divide the ones. he needs to bring down the 8 and keep dividing. \\(\

$$\begin{array}{r}14 \\\\ 4\\enclose{longdiv}{568} \\\\ \\underline{-\\ 4\\ \\ \\ } \\\\ 16 \\\\ \\underline{-\\ 16\\ \\ } \\\\ 0 \\\\ \\end{array}$$

\\)

Explanation:

To determine Noah's mistake, we analyze the long - division of \(568\div4\). In long - division, we divide digit by digit starting from the leftmost digit. After dividing the hundreds and tens place (we get a remainder of 0 after dividing the tens place as \(16\div4 = 4\)), we still have the digit 8 in the ones place. We need to bring down the 8 and divide \(8\) by \(4\) (which gives \(2\)) and place this \(2\) in the ones place of the quotient. Noah's quotient is \(14\), but he didn't consider the ones place digit. He should have continued the division to include the ones place. The first option's reasoning about 1 hundred is incorrect because when dividing \(568\) by \(4\), we start with the hundreds place (\(5\div4\), but actually we group the digits as \(56\) tens and \(8\) ones or we do the division digit - by - digit: \(5\div4\) gives a quotient of \(1\) (in the hundreds place) with a remainder of \(1\), then we bring down the \(6\) to make \(16\) (in the tens place), \(16\div4 = 4\) (in the tens place), and then we bring down the \(8\) (in the ones place) and \(8\div4=2\) (in the ones place). So the correct quotient is \(142\), and Noah's mistake was that he didn't divide the ones place (he didn't bring down the \(8\) and continue the division).

Answer:

Noah didn't divide the ones. He needs to bring down the 8 and keep dividing.