Question

there is a division arithmetic expression: \\(\

$$\begin{array}{r} \\\\ 15 \\enclose{longdiv}{109} \\\\ -000 \\\\ \\hline 109 \\\\ -000 \\\\ \\hline 109 \\\\ \\end{array}$$

\\) (the top of the division has a blank to fill in, with a number selection panel of 0 - 9 on the right, and a number line from 0 to 200 on the far right, with 0 and 100 marked).

Explanation:

Step1: Analyze division structure

We have long division: $15 \enclose{longdiv}{109}$, with a placeholder digit for the quotient's tens place (the leftmost 0 in the 000 quotient). We need to find what digit replaces the empty box to make the subtraction valid.

Step2: Determine valid quotient digit

The first step of dividing 109 by 15: 15 does not go into 1, nor 10, so we look at 109. The largest multiple of 15 less than 109 is $15 \times 7 = 105$, but wait, the subtraction shown is $109 - 000 = 109$, which means the first digit of the quotient (tens place) is 0 (since 15 can't go into 10 tens, so we write 0 in the tens place, then move to the ones place). The empty box is the tens digit of the quotient, which must be 0.

Answer:

0