Question

continue dividing on the algorithm. 9 ones is equivalent to 90 tenths. divide 90 tenths by 12 ones, then multiply and subtract to show how many tenths you have left.
\

$$\begin{array}{r}0.\\square \\\\ 12 \\enclose{longdiv}{9.0}\\\\ -\\square\\square \\\\ \\hline \\ \\ \\ \\ \\square \\\\ \\end{array}$$

Explanation:

Step1: Find how many times 12 goes into 90 tenths

We know that 9 ones is 90 tenths. We divide 90 by 12. \( 12\times7 = 84 \), and \( 12\times8=96 \) which is more than 90, so the quotient digit in tenths place is 7.

Step2: Multiply 12 by 7

\( 12\times7 = 84 \), so we subtract 84 (which is 84 tenths) from 90 tenths.

Step3: Subtract to find the remainder

\( 90 - 84=6 \) tenths.

So the division algorithm becomes:
\(
equire{enclose}

$$\begin{array}{r} 0.\boldsymbol{7} \\ 12 \enclose{longdiv}{9.0} \\ \underline{- \boldsymbol{8}.\boldsymbol{4}} \\ \boldsymbol{0.6} \\ \end{array}$$

\)

Answer:

The digit in the tenths place of the quotient is 7, the number subtracted is \( 8.4 \) (or 84 tenths), and the remainder is \( 0.6 \) (or 6 tenths). So filling in the boxes: the first box (tenths place of quotient) is 7, the next two boxes (subtracted number) are 8 and 4, and the last box (remainder) is 6. So the completed division is:

\(

$$\begin{array}{r} 0.\boxed{7} \\ 12 \enclose{longdiv}{9.0} \\ \underline{- \boxed{8}.\boxed{4}} \\ \boxed{0.6} \\ \end{array}$$

\) (Note: If we consider the remainder in tenths without the decimal for the last box, it could also be 6, but in the context of the division with decimals, \( 0.6 \) is more appropriate as the remainder here represents 6 tenths which is \( 0.6 \) in decimal form.)