Let number be $x$. $\frac{4}{5}x - \frac{3}{4}x = 4 \implies \frac{16x-15x}{20} = 4 \implies \frac{x}{20} = 4 \implies x = 80$.

Decimal values: $\frac{7}{3} = 2.33, \frac{25}{7} = 3.57, \frac{35}{9} = 3.88, \frac{19}{2} = 9.5$. The largest is $\frac{19}{2}$.

Let the fraction be $x$. According to question: $x \cdot x \div \frac{1}{x} = 3\frac{13}{81} \implies x^2 \cdot x = \frac{256}{81} \implies x^3 = \frac{256}{81}$. The fraction $3\frac{13}{81} = \frac{256}{81}$ is not a perfect cube (not $(4/3)^3$). However, following book solution, $x = 4/3$.

$\frac{1}{2}\% = 0.5\% = \frac{0.5}{100} = 0.005$.

Let the fraction be $\frac{x}{55-x} = \frac{3}{8} \implies 8x = 165 - 3x \implies 11x = 165 \implies x = 15$. So the fraction is $\frac{15}{40}$, which is not in the options.

Terms: $1 + (1-\frac{1}{2}) + (\frac{1}{2}-\frac{1}{3}) + ... + (\frac{1}{10}-\frac{1}{11}) = 1 + 1 - \frac{1}{11} = 2 - \frac{1}{11} = \frac{21}{11}$. Book answer is (1) $11/10$.

Let fraction be $x$. $x^2 \div \frac{1}{x} = x^3 = 18\frac{26}{27} = \frac{512}{27} = (\frac{8}{3})^3 = (2\frac{2}{3})^3$. The answer should be $8/3$. Book says $1\frac{1}{3} = 4/3$ which is not $x^3$. Check.

Let fraction be $\frac{x}{y}$. $\frac{x+1}{y+1} = \frac{2}{3} \implies 3x+3 = 2y+2 \implies 2y-3x = 1$. $\frac{x-1}{y-1} = \frac{1}{2} \implies 2x-2 = y-1 \implies y = 2x-1$. Substitution: $2(2x-1) - 3x = 1 \implies 4x-2-3x = 1 \implies x = 3$. $y = 2(3)-1 = 5$. Fraction is $\frac{3}{5}$.

Solution: $1-\frac{1}{2} = \frac{1}{2} \implies 1+\frac{1}{1/2} = 1+2 = 3 \implies 1+\frac{1}{3} = \frac{4}{3} \implies 1+\frac{1}{4/3} = 1+\frac{3}{4} = \frac{7}{4}$. Book answer is (4), there might be a typo.

Decimal values: $\frac{24}{25} = 0.96, \frac{10}{11} = 0.90, \frac{99}{100} = 0.99, \frac{68}{69} = 0.98$. The smallest value is $\frac{10}{11}$.

Values: $\sqrt{\frac{9}{49}} = \frac{3}{7} \approx 0.428$, $\frac{4}{9} \approx 0.44$, $0.45$, $(0.8)^2 = 0.64$. Largest is 0.64.

Solution: From bottom: $1+\frac{1}{2}=\frac{3}{2} \implies 1+\frac{1}{3/2} = 1+\frac{2}{3} = \frac{5}{3} \implies 1+\frac{1}{5/3} = 1+\frac{3}{5} = \frac{8}{5} \implies 1+\frac{1}{8/5} = 1+\frac{5}{8} = \frac{13}{8}$. Book answer is (2) $\frac{10}{11}$, might be different in source.

Note: Values for option (2) are $\frac{3}{2}=1.5, \frac{1}{4}=0.25, \frac{2}{3}=0.66, \frac{2}{5}=0.4$. Descending order (largest to smallest): $\frac{3}{2} > \frac{2}{3} > \frac{2}{5} > \frac{1}{4}$. There might be an error in the book options, answer (2) is marked.

Let numerator $= x$, denominator $= x+8$. Fraction $= \frac{x}{x+8}$. According to question: $\frac{x+17}{x+8-1} = \frac{3}{2} \implies \frac{x+17}{x+7} = \frac{3}{2} \implies 2x+34 = 3x+21 \implies x = 13$. Thus, the number is $\frac{13}{13+8} = \frac{13}{21}$.

Decimal values: $\frac{16}{21} \approx 0.76, \frac{11}{14} \approx 0.78, \frac{17}{19} \approx 0.89$. Ascending order: $0.76 < 0.78 < 0.89$. The correct answer is option (2).

1 day = 24 hours = $24 \times 60$ minutes = 1440 minutes. Fraction of 45 minutes = $\frac{45}{1440} = \frac{1}{32}$.

Calculating the decimal values: $\frac{2}{7} \approx 0.28, \frac{3}{13} \approx 0.23, \frac{5}{6} \approx 0.83$. Therefore, the descending order (largest to smallest) is $\frac{5}{6}, \frac{2}{7}, \frac{3}{13}$.

$\frac{1}{2}+\frac{2}{3} = \frac{3+4}{6} = \frac{7}{6} = 1.166...$ The book provides solution for $\frac{1}{2} + \frac{1}{3} = 5/6 = 0.833...$. The question likely should have been $(\frac{1}{2}+\frac{1}{3})$.

$\frac{-24}{20} = \frac{-6}{5}$. To make the denominator 25, multiply by 5: $\frac{-6 \times 5}{5 \times 5} = \frac{-30}{25}$.

$\frac{13}{5^4} = \frac{13}{625} = \frac{13 \times 2^4}{5^4 \times 2^4} = \frac{13 \times 16}{10000} = \frac{208}{10000} = 0.0208$. The options in the book seem incorrect or calculation differs. Book answer is (4) 0.104.