Question

homework: module a part 1 review
score: 19/30 answered: 19/30
question 20
in the following exercise, perform the indicated operation and simplify.
$left(\frac{1}{6}+\frac{8}{11}
ight)divleft(\frac{4}{9}-\frac{11}{15}
ight)$
question help: written example post to forum

Explanation:

Step1: Calculate the sum in the first - parentheses

Find a common denominator for $\frac{1}{6}$ and $\frac{8}{11}$. The common denominator of 6 and 11 is 66.
$\frac{1}{6}+\frac{8}{11}=\frac{1\times11}{6\times11}+\frac{8\times6}{11\times6}=\frac{11 + 48}{66}=\frac{59}{66}$

Step2: Calculate the difference in the second - parentheses

Find a common denominator for $\frac{4}{9}$ and $\frac{11}{15}$. The common denominator of 9 and 15 is 45.
$\frac{4}{9}-\frac{11}{15}=\frac{4\times5}{9\times5}-\frac{11\times3}{15\times3}=\frac{20 - 33}{45}=-\frac{13}{45}$

Step3: Divide the two results

Dividing by a fraction is the same as multiplying by its reciprocal.
$\frac{59}{66}\div(-\frac{13}{45})=\frac{59}{66}\times(-\frac{45}{13})=-\frac{59\times45}{66\times13}=-\frac{59\times15}{22\times13}=-\frac{885}{286}$

Answer:

$-\frac{885}{286}$