Arrange each of the following in decreasing order. \( \begin{array}{ll}\text { a. } \frac{10}{13}, \frac{10}{19}, \frac{10}{21} & \text { b. }-\frac{23}{25},-\frac{11}{16},-\frac{1}{5} \\ \text { a. Choose the sequence that is written in decreasing order. } \\ \begin{array}{llll}\text { A. } \frac{10}{19}, \frac{10}{13}, \frac{10}{21} & \text { B. } \frac{10}{13}, \frac{10}{21}, \frac{10}{19} & \text { C. } \frac{10}{13}, \frac{10}{19}, \frac{10}{21} & \text { D. } \frac{10}{21}, \frac{10}{19}, \frac{10}{13}\end{array}\end{array} \)

To arrange the fractions in decreasing order, we can first convert them to decimals to compare them easily: - \( \frac{10}{13} \approx 0.7692 \) - \( \frac{10}{19} \approx 0.5263 \) - \( \frac{10}{21} \approx 0.4762 \) Now, from the highest to the lowest value, we have: 1. \( \frac{10}{13} \) 2. \( \frac{10}{19} \) 3. \( \frac{10}{21} \) So the correct decreasing order is \( \frac{10}{13}, \frac{10}{19}, \frac{10}{21} \), which corresponds to option C. For the negative fractions, we have: - \( -\frac{23}{25} = -0.92 \) - \( -\frac{11}{16} \approx -0.6875 \) - \( -\frac{1}{5} = -0.2 \) Arranging these in decreasing order (least negative to most negative): 1. \( -\frac{1}{5} \) 2. \( -\frac{11}{16} \) 3. \( -\frac{23}{25} \) So for part b, the correct order is \( -\frac{1}{5}, -\frac{11}{16}, -\frac{23}{25} \).