Full solution

\frac{9}{10}\times1\frac{1}{4}\times2\frac{2}{3}=

Convert to Improper Fractions: First, convert the mixed numbers to improper fractions to make the multiplication easier. $\newline$ $1\frac{1}{4}$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator, then placing the result over the original denominator. $\newline$ $1\frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}$
Multiply Fractions: Similarly, convert $2\frac{2}{3}$ to an improper fraction. $\newline$ $2\frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}$
Calculate Numerator Product: Now, multiply the three fractions together: $\frac{9}{10} \times \frac{5}{4} \times \frac{8}{3}$ . $\newline$ First, multiply the numerators together: $9 \times 5 \times 8$ .
Calculate Denominator Product: Calculate the product of the numerators: $9 \times 5 \times 8 = 45 \times 8 = 360$ .
Write Result as Fraction: Next, multiply the denominators together: $10 \times 4 \times 3$ .
Simplify Fraction: Calculate the product of the denominators: $10 \times 4 \times 3 = 40 \times 3 = 120$ .
Final Answer: Now, write the result as a fraction: $\frac{360}{120}$ .
Final Answer: Now, write the result as a fraction: $\frac{360}{120}$ .Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $120$ in this case. $\newline$ $\frac{360}{120} = \frac{360 \div 120}{120 \div 120} = \frac{3}{1}$ .
Final Answer: Now, write the result as a fraction: $\frac{360}{120}$ .Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $120$ in this case. $\newline$ $\frac{360}{120} = \frac{360 \div 120}{120 \div 120} = \frac{3}{1}$ .Since $\frac{3}{1}$ is equal to $3$ , the final answer is $3$ .