Product, sum and quotient

If the product of 1 1/6 and 3 2/3 is added to the quotient of 5/7 and 6/7, what is the sum? Write the solution as a mixed number or a fraction in the lowest terms.

Final Answer:

s =  5 ¹⁄₉ = 46/9

Step-by-step explanation:

$$\begin{gathered} a=1\frac{1}{6}=1+\frac{1}{6}=\frac{1\cdot 6+1}{6}=\frac{6+1}{6}=\frac{7}{6}=1\frac{1}{6}\doteq 1.1667 \\ b=3\frac{2}{3}=3+\frac{2}{3}=\frac{3\cdot 3+2}{3}=\frac{9+2}{3}=\frac{11}{3}=3\frac{2}{3}\doteq 3.6667 \\ p=a\cdot b=\frac{7}{6}\cdot \frac{11}{3}=\frac{7\cdot 11}{6\cdot 3}=\frac{77}{18}\doteq 4.2778 \\ q=\frac{5}{7}/\frac{6}{7}=\frac{5}{7}:\frac{6}{7}=\frac{5}{7}\cdot \frac{7}{6}=\frac{5\cdot 7}{7\cdot 6}=\frac{35}{42}=\frac{5}{6}\doteq 0.8333 \\ s=p+q=\frac{77}{18}+\frac{5}{6}=\frac{77}{18}+\frac{15}{18}=\frac{77+15}{18}=\frac{92}{18}=\frac{46}{9}=5\frac{1}{9}=5.1111 \end{gathered}$$

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