Solve the expression: 14 - 13.2 : (3$$\frac{11}{21}$$ - 2$$\frac{4}{25}$$)

Okay, let's solve this step by step. First, we need to convert the mixed numbers to improper fractions. $$3\frac{11}{21} = \frac{3 \times 21 + 11}{21} = \frac{63 + 11}{21} = \frac{74}{21}$$ $$2\frac{4}{25} = \frac{2 \times 25 + 4}{25} = \frac{50 + 4}{25} = \frac{54}{25}$$ Now we subtract these fractions: $$\frac{74}{21} - \frac{54}{25}$$ To subtract them, we need a common denominator. The least common multiple of 21 and 25 is 525. So we convert each fraction to have this denominator. $$\frac{74}{21} = \frac{74 \times 25}{21 \times 25} = \frac{1850}{525}$$ $$\frac{54}{25} = \frac{54 \times 21}{25 \times 21} = \frac{1134}{525}$$ Now we subtract: $$\frac{1850}{525} - \frac{1134}{525} = \frac{1850 - 1134}{525} = \frac{716}{525}$$ Next, we perform the division: 13.2 : $$\frac{716}{525}$$. First, convert 13.2 to a fraction: $$13.2 = \frac{132}{10} = \frac{66}{5}$$. Now divide: $$\frac{66}{5} : \frac{716}{525} = \frac{66}{5} \times \frac{525}{716} = \frac{66 \times 525}{5 \times 716} = \frac{34650}{3580}$$ Simplify the fraction by dividing both numerator and denominator by 10: $$\frac{3465}{358}$$. Now, we can simplify further by dividing both by 5: $$\frac{3465}{358} = \frac{693}{71.6}$$ or $$\frac{693 \times 5}{716} = \frac{3465}{716}$$ (already simplified) Calculate the division: $$\frac{34650}{3580} = 9.67877 \approx 9.68$$ or leave as an improper fraction $$\frac{3465}{358}$$. Reducing the fraction: $$\frac{66}{5} \times \frac{525}{716} = \frac{66 \times 105}{716} = \frac{33 \times 105}{358} = \frac{3465}{358}$$ So, 14 - $$\frac{3465}{358}$$. We convert 14 to a fraction with a denominator of 358. $$14 = \frac{14 \times 358}{358} = \frac{5012}{358}$$ Now subtract: $$\frac{5012}{358} - \frac{3465}{358} = \frac{5012 - 3465}{358} = \frac{1547}{358}$$ The answer is $$\frac{1547}{358}$$. As a decimal approximation, this is about 4.32. Answer: $$\frac{1547}{358}$$