Quotient of two fractions

If the quotient of 8/9 and 1/3 is subtracted from the product of 2 3/4 and 1 3/5, what is the difference? Write the solution as a mixed number or a fraction in the lowest terms.

Final Answer:

x =  -26/15

Step-by-step explanation:

$$\begin{gathered} q=\frac{8}{9}/\frac{1}{3}=\frac{8}{9}:\frac{1}{3}=\frac{8}{9}\cdot \frac{3}{1}=\frac{8\cdot 3}{9\cdot 1}=\frac{24}{9}=\frac{8}{3}=2\frac{2}{3}\doteq 2.6667 \\ a=2\frac{3}{4}=2+\frac{3}{4}=\frac{2\cdot 4+3}{4}=\frac{8+3}{4}=\frac{11}{4}=2\frac{3}{4}=2.75 \\ b=1\frac{3}{5}=1+\frac{3}{5}=\frac{1\cdot 5+3}{5}=\frac{5+3}{5}=\frac{8}{5}=1\frac{3}{5}=1.6 \\ p=a\cdot b=\frac{11}{4}\cdot \frac{8}{5}=\frac{11\cdot 8}{4\cdot 5}=\frac{88}{20}=\frac{22}{5}=4\frac{2}{5}=4.4 \\ x=q-p=\frac{8}{3}-\frac{22}{5}=\frac{40}{15}-\frac{66}{15}=\frac{40-66}{15}=\frac{-26}{15}=-\frac{26}{15}=-1\frac{11}{15}=-1.7333 \end{gathered}$$

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