Question

caleb uses the standard algorithm to find 438 ÷ 6. part of his work is shown. what do the 7 and 1 represent in calebs work? 43 tens divided by 6 is 7 tens with a remainder of 1 ten. what should caleb do next? bring down the \square to show there is 1 ten and? ones that still need to be divided. \

$$\begin{array}{r}7 \\\\ 6 \\overline{) 438} \\\\ - 42 \\\\ \\hline 1 \\\\ \\end{array}$$

Explanation:

First Sub - Question (What do 7 and 1 represent)

In the standard division algorithm for \(438\div6\), we start by looking at the tens place. The number formed by the first two digits is 43 (which is 43 tens). When we divide 43 tens by 6, we find out how many groups of 6 we can make from 43 tens. \(6\times7 = 42\), so we can make 7 groups of 6 tens (which is 7 tens), and the remainder is \(43 - 42=1\) ten. So 7 represents the number of groups of 6 tens (7 tens) and 1 represents the remaining 1 ten.

In the standard long - division algorithm, after finding the remainder in the tens place, we bring down the digit from the ones place to combine with the remainder in the tens place to form a new number for further division. In the number 438, the digit in the ones place is 8. So we bring down the 8. After bringing down the 8, the remainder 1 (in the tens place) and the 8 (in the ones place) form 18, and then we can divide 18 by 6. Also, the number of ones in 1 ten and 8 ones is 18, but for the first blank (the digit to bring down) is 8, and the number of ones is 8 (wait, actually, when we bring down the 8, we have 1 ten and 8 ones, so the number of ones is 8? Wait, no. Wait, 1 ten is 10, and 8 ones is 8, so together it's 18. But the question says "to show there is 1 ten and? ones that still need to be divided". Since we bring down the 8, the number of ones is 8. So we bring down the 8, and the number of ones is 8.

Answer:

7 represents 7 tens (the number of groups of 6 tens in 43 tens), and 1 represents 1 ten (the remainder when 43 tens is divided by 6).

Second Sub - Question (What should Caleb do next)