​Which one is the largest among the fractions $$\left(\frac{4}{9}\right),\left(\frac{5}{8}\right),\left(\frac{2}{3}\right) \text { and }\left(\frac{3}{4}\right)$$​ ?​

Correct option is D

Given:

$$\frac{4}{9}, \frac{5}{8}, \frac{2}{3},$$​ and $$\frac{3}{4}$$​ 

Solution:

Compare $$\frac{4}{9}$$​ and $$\frac{5}{8}$$ :​

Cross-multiply:

$$4 \times 8 = 32 \quad \text{and} \quad 5 \times 9$$​ = 45

Since 32 < 45, we can conclude that:

​$$\frac{4}{9} < \frac{5}{8}$$​​

Compare $$\frac{5}{8}$$​ and $$\frac{2}{3}$$ :​

Cross-multiply:

$$5 \times 3$$​ = 15$$\quad \text{and} \quad 2 \times 8$$​ = 16

Since 15 < 16, we can conclude that:

​$$\frac{5}{8} < \frac{2}{3}$$​​

Compare $$\frac{2}{3}$$​ and $$\frac{3}{4}$$​​

Cross-multiply:

$$2 \times 4 = 8 \quad \text{and} \quad 3 \times 3$$​ = 9

Since 8 < 9, we can conclude that:

​$$\frac{2}{3} < \frac{3}{4}$$​​

From the comparisons:

​$$\frac{4}{9} < \frac{5}{8} < \frac{2}{3} < \frac{3}{4}$$​​

Thus, $$\frac{3}{4}$$​ is the largest fraction among the given options.

Thus, the correct option is (d)​$$\frac{3}{4}$$