Simplify \(\displaystyle 2\frac{3}{4}\div2\frac{2}{3}\div1\frac{1}{12}=?\)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{99}{104}\)
Change each mixed number into an improper fraction. Then dividing by a fraction is the same as multiplying by its reciprocal, and the divisions are done from left to right.
\(\displaystyle 2\frac{3}{4}=\frac{11}{4},\quad 2\frac{2}{3}=\frac{8}{3},\quad 1\frac{1}{12}=\frac{13}{12}\)
\(\displaystyle \frac{11}{4}\div\frac{8}{3}\div\frac{13}{12}=\frac{11}{4}\times\frac{3}{8}\times\frac{12}{13}\)
\(\displaystyle =\frac{11\times3\times12}{4\times8\times13}=\frac{396}{416}=\frac{99}{104}\)