Question

Evaluate the expression. Write fraction in simplest form.

$\frac{{\displaystyle \frac{7}{6}}}{\left(-{\displaystyle \frac{11}{5}}\right)\left(10{\displaystyle \frac{1}{2}}\right)\left(-{\displaystyle \frac{5}{11}}\right)}$

Answer 1

Step 1: $\frac{{\displaystyle \frac{7}{6}}}{\left(-{\displaystyle \frac{11}{5}}\right)\left(10{\displaystyle \frac{1}{2}}\right)\left(-{\displaystyle \frac{5}{11}}\right)}=\frac{{\displaystyle \frac{7}{6}}}{\left(-{\displaystyle \frac{11}{5}}\right)\left({\displaystyle \frac{21}{2}}\right)\left(-{\displaystyle \frac{5}{11}}\right)}$

$=\frac{{\displaystyle \frac{7}{6}}}{{\displaystyle \frac{(-11)\times 21\times (-5)}{5\times 2\times 11}}}=\frac{{\displaystyle \frac{7}{6}}}{{\displaystyle \frac{21}{2}}}$

Step 2: $a÷b=a\times \frac{1}{b}$

$\frac{{\displaystyle \frac{7}{6}}}{{\displaystyle \frac{21}{2}}}=\frac{7}{6}\times \frac{2}{21}=\frac{1}{9}$

Step 3: In simplest form $\frac{1}{9}$ as 1 & 9 have no common factor other than 1.

Final Answer: The value of expression in simplest form is $\frac{1}{9}$.