Question

which fraction and decimal forms match the long division problem?
(the long division process: 15 divides 7.000, first step: 15×0.4 = 6.0, subtract 6.0 from 7.0 to get 1.0, bring down a 0 to make 10.0? wait, no, the given long division steps are: 15)7.000, -60 (wait, maybe typo, should be -6.0? then 100 (1.00), -90 (0.90), 100 (0.100), -90 (0.090), 10. then the options are:
a. \\(\frac{7}{15}\\) and 0.46
b. \\(\frac{15}{7}\\) and 0.466
c. \\(\frac{15}{7}\\) and 0.4\\(\overline{6}\\)
d. \\(\frac{7}{15}\\) and 0.4\\(\overline{6}\\))

Explanation:

Step1: Identify the fraction

The long division shows $7.000 \div 15$, so the fraction is $\frac{7}{15}$.

Step2: Analyze the decimal result

From the division, after the first two digits, the remainder 10 repeats, leading to a repeating 6. So the decimal is $0.4\overline{6}$.

Step3: Match with options

Option D has both $\frac{7}{15}$ and $0.4\overline{6}$, which matches.

Answer:

D. $\frac{7}{15}$ and $0.4\overline{6}$