Question

(11 19/48-9 11/32)+(-8-4 5/12)

Answer 1

(11 19/48-9 11/32)+(-8-4 5/12)=
-10 35/96
1) 11 19/48-9 11/32=11 38/96-9 33/96=
2 5/96
2)-8-4 5/12=-12 5/12
3)2 5/96-12 5/12=2 5/96-12 40/96=
-10 35/96

Answer 2

Let's break down the expression step by step:

1. $11 \frac{19}{48} - 9 \frac{11}{32}$
2. $(-8) - 4 \frac{5}{12}$

First, let's simplify each part:

For the first part, $11 \frac{19}{48} - 9 \frac{11}{32}$: To subtract fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 48 and 32 is 96.

11 \frac{19}{48} &= \frac{11 \cdot 48 + 19}{48} = \frac{547}{48} \\ 9 \frac{11}{32} &= \frac{9 \cdot 32 + 11}{32} = \frac{299}{32} \end{align*}\] Now we can subtract these two fractions: \[\frac{547}{48} - \frac{299}{32} = \frac{547 \cdot 2}{48 \cdot 2} - \frac{299 \cdot 3}{32 \cdot 3} = \frac{1094}{96} - \frac{897}{96} = \frac{197}{96}\] For the second part, \((-8) - 4 \frac{5}{12}\): Convert the mixed number to an improper fraction: \[4 \frac{5}{12} = \frac{4 \cdot 12 + 5}{12} = \frac{53}{12}\] Now we can subtract: \((-8) - \frac{53}{12} = -\frac{8 \cdot 12}{12} - \frac{53}{12} = -\frac{149}{12}\) Now we can add the two results together: \[\frac{197}{96} - \frac{149}{12}\] To add these fractions, we need a common denominator. The least common multiple (LCM) of 96 and 12 is 288. \[\frac{197}{96} = \frac{197 \cdot 3}{96 \cdot 3} = \frac{591}{288}\] \[-\frac{149}{12} = -\frac{149 \cdot 24}{12 \cdot 24} = -\frac{3576}{288}\] Now we can add these two fractions: \[\frac{591}{288} - \frac{3576}{288} = \frac{591 - 3576}{288} = -\frac{2985}{288}\] So, the final result is \(-\frac{2985}{288}\).