Question

$\frac{1}{4\frac{2}{7}}+\frac{1}{3\frac{11}{13}}+\frac{1}{\frac{5}{9}}=$

• A. 312/45
• B. 513/13
• C. 218/35
• D. 172/75

Answer 1

Answer:

D. 172/75

Convert mixed fractions to improper fractions:

$4\frac{2}{7} = \frac{30}{7}, \quad 3\frac{11}{13} = \frac{50}{13}$

Now take reciprocals:

$\frac{1}{4\frac{2}{7}} = \frac{7}{30}, \quad \frac{1}{3\frac{11}{13}} = \frac{13}{50}, \quad \frac{1}{\frac{5}{9}} = \frac{9}{5}$

So expression becomes:
$\frac{7}{30} + \frac{13}{50} + \frac{9}{5}$

LCM of 30, 50, 5 = 150

Convert:
$\frac{7}{30} = \frac{35}{150}, \quad \frac{13}{50} = \frac{39}{150}, \quad \frac{9}{5} = \frac{270}{150}$

Add:
$\frac{35 + 39 + 270}{150} = \frac{344}{150}$

Simplify:
$\frac{344}{150} = \frac{172}{75}$