Question

write \\(\frac{9}{12}\\) as a decimal. start by filling in the algorithm.

Explanation:

Step1: Simplify the fraction

First, simplify \(\frac{9}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So \(\frac{9\div3}{12\div3}=\frac{3}{4}\).

Step2: Perform long division

To convert \(\frac{3}{4}\) to a decimal, we do the long division of 3 by 4. In the long - division algorithm, we set it up as \(4\enclose{longdiv}{3.0}\) (we add a decimal point and a zero to the dividend since 3 is less than 4). 4 goes into 30 seven times (\(4\times7 = 28\)), subtract 28 from 30, we get a remainder of 2. Then we add another zero, making it 20. 4 goes into 20 exactly 5 times (\(4\times5=20\)). So putting it all together, \(\frac{3}{4}=0.75\). But for the long - division setup in the problem (the algorithm box), we are dividing 9 by 12, so the divisor is 12 and the dividend is 9 (we can also think of it as \(12\enclose{longdiv}{9.00}\)). When we do \(12\enclose{longdiv}{9.0}\), 12 goes into 90 seven times (\(12\times7 = 84\)), remainder 6. Then 12 goes into 60 five times (\(12\times5 = 60\)). So the long - division setup has divisor 12 and dividend 9 (or 9.0). So in the first box (divisor) we put 12 and in the dividend box we put 9. But if we consider the initial simplification, \(\frac{9}{12}=\frac{3}{4}\), and the long - division for \(\frac{3}{4}\) is \(4\enclose{longdiv}{3}\). But based on the original fraction \(\frac{9}{12}\), the divisor is 12 and the dividend is 9. So for the algorithm (the division box), the divisor is 12 and the dividend is 9. So in the first (divisor) box, we put 12, and in the dividend box, we put 9.

Answer:

The divisor box (the first box) should have 12 and the dividend box should have 9. If we are just looking at the first step of the long - division algorithm for \(\frac{9}{12}\), the divisor is 12 and the dividend is 9. So the number in the divisor box (the left - most box) is 12 and the number in the dividend box (the box inside the division symbol) is 9.