To solve the expression \(-4 \frac{1}{6} - 7 \frac{3}{4}\), we can follow these steps:
-
Convert the mixed numbers to improper fractions.
-
For \(-4 \frac{1}{6}\): \[ -4 \frac{1}{6} = -\left(4 \times 6 + 1\right)/6 = -\frac{24 + 1}{6} = -\frac{25}{6} \]
-
For \(-7 \frac{3}{4}\): \[ -7 \frac{3}{4} = -\left(7 \times 4 + 3\right)/4 = -\frac{28 + 3}{4} = -\frac{31}{4} \]
-
-
Now, we need to subtract these fractions: \[ -\frac{25}{6} - \frac{31}{4} \]
-
To perform the subtraction, we need a common denominator. The least common multiple of 6 and 4 is 12.
-
Convert both fractions to have a denominator of 12:
-
For \(-\frac{25}{6}\): \[ -\frac{25}{6} = -\frac{25 \times 2}{6 \times 2} = -\frac{50}{12} \]
-
For \(-\frac{31}{4}\): \[ -\frac{31}{4} = -\frac{31 \times 3}{4 \times 3} = -\frac{93}{12} \]
-
-
Now, we can subtract these fractions: \[ -\frac{50}{12} - \frac{93}{12} = -\frac{50 + 93}{12} = -\frac{143}{12} \]
-
Finally, we can convert \(-\frac{143}{12}\) back to a mixed number: \[ 143 \div 12 = 11 \quad \text{(remainder 11)} \] Thus, \(-\frac{143}{12} = -11 \frac{11}{12}\).
So, the final answer is:
\(-11 \frac{11}{12} = [11][11][12]\).