Question

8 3/4 +(13 5/12- 2 11/18)

Answer 1

$8\frac{3}{4}+(13\frac{5}{12}-2\frac{11}{18})=\frac{35}{4}+(\frac{161}{12}-\frac{47}{18})=\frac{35}{4}+\frac{389}{36}=\frac{176}{9}=19\frac{5}{9}$

Answer 2

To solve the given expression, let's break it down step by step:

1. Inside the parentheses:

   • Subtract the mixed numbers inside the parentheses:
     • $13 \frac{5}{12} - 2 \frac{11}{18}$

   To subtract mixed numbers, we first convert them to improper fractions:

   $13 \frac{5}{12} = \frac{12 \cdot 13 + 5}{12} = \frac{156 + 5}{12} = \frac{161}{12}$

   $2 \frac{11}{18} = \frac{18 \cdot 2 + 11}{18} = \frac{36 + 11}{18} = \frac{47}{18}$

   Now, subtract:

   $\frac{161}{12} - \frac{47}{18}$

   To subtract fractions, we need a common denominator, which in this case is $36$ (the least common multiple of $12$ and $18$):

   $\frac{161 \cdot 3}{12 \cdot 3} - \frac{47 \cdot 2}{18 \cdot 2} = \frac{483}{36} - \frac{94}{36} = \frac{389}{36}$

2. Now we have: $8 \frac{3}{4} + \frac{389}{36}$

   Convert $8 \frac{3}{4}$ to an improper fraction:

   $8 \frac{3}{4} = \frac{8 \cdot 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4}$

   Now add:

   $\frac{35}{4} + \frac{389}{36}$

   To add these fractions, we need a common denominator, which is $36$ (the least common multiple of $4$ and $36$):

   $\frac{35 \cdot 9}{4 \cdot 9} + \frac{389}{36} = \frac{315}{36} + \frac{389}{36} = \frac{704}{36}$

   Reduce the fraction:

   $\frac{704}{36} = \frac{176}{9}$

So, $8 \frac{3}{4} + \left(13 \frac{5}{12} - 2 \frac{11}{18}\right) = \frac{176}{9}$ or approximately $19.56$.