Discussion
Arrange the following in descending order of their magnitude :
1. \(\dfrac{5}{7}\)
2. \(\dfrac{3}{4}\)
3. \(\dfrac{5}{6}\)
4. \(\dfrac{8}{9}\)
Answer: C
The descending order is 4, 3, 2, 1.
Convert each fraction to a decimal:
\[ \begin{aligned} \tfrac{8}{9} &\approx 0.889, \quad \tfrac{5}{6} \approx 0.833 \\ \tfrac{3}{4} &= 0.75, \quad \tfrac{5}{7} \approx 0.714 \end{aligned} \]
So 8/9 > 5/6 > 3/4 > 5/7. Each of these fractions is 1 minus a unit-like gap (1/9, 1/6, 1/4, 2/7), and the smaller the gap, the larger the fraction. The option 1, 2, 3, 4 is the ascending order, and the other two options misplace 3/4 or 5/7.
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