Question

Arrange the following rational numbers in ascending order:
(A) \(-\frac{4}{5}\)
(B) \(-\frac{5}{12}\)
(C) \(-\frac{7}{18}\)
(D) \(-\frac{2}{3}\)
Choose the correct answer from the options given below

• A. (A), (B), (D), (C)
• B. (C), (D), (B), (A)
• C. (A), (D), (B). (C)
• D. (D), (C), (B), (A)

Answer 1

The Correct Option is B

To arrange the given rational numbers in ascending order, we first need to compare them. The numbers are: \(-\frac{4}{5}\), \(-\frac{5}{12}\), \(-\frac{7}{18}\), \(-\frac{2}{3}\).

To make the comparison easier, let's convert all the fractions to have a common denominator. The least common multiple (LCM) of the denominators 5, 12, 18, and 3 is 180. 

1. Convert \(-\frac{4}{5}\):
   • \(-\frac{4}{5} = -\frac{4 \times 36}{5 \times 36} = -\frac{144}{180}\)
2. Convert \(-\frac{5}{12}\):
   • \(-\frac{5}{12} = -\frac{5 \times 15}{12 \times 15} = -\frac{75}{180}\)
3. Convert \(-\frac{7}{18}\):
   • \(-\frac{7}{18} = -\frac{7 \times 10}{18 \times 10} = -\frac{70}{180}\)
4. Convert \(-\frac{2}{3}\):
   • \(-\frac{2}{3} = -\frac{2 \times 60}{3 \times 60} = -\frac{120}{180}\)

Now, we have the fractions with a common denominator: \(-\frac{144}{180}\), \(-\frac{75}{180}\), \(-\frac{70}{180}\), \(-\frac{120}{180}\).

Next, we arrange these fractions in ascending order. Since all are negative, the fraction with the smallest absolute value is the greatest (least negative value):

• \(-\frac{70}{180}\) 
  (C) \(-\frac{7}{18}\)
• \(-\frac{75}{180}\) 
  (D) \(-\frac{5}{12}\)
• \(-\frac{120}{180}\) 
  (B) \(-\frac{2}{3}\)
• \(-\frac{144}{180}\) 
  (A) \(-\frac{4}{5}\)

Therefore, the correct order is: \(-\frac{7}{18}, -\frac{5}{12}, -\frac{2}{3}, -\frac{4}{5}\)

Hence, the correct answer is

(C), (D), (B), (A)

.