(4 5/9-3 7/12):(-1 8/27)=

To solve the expression \((4 \frac{5}{9} - 3 \frac{7}{12}) : (-1 \frac{8}{27})\), we will perform the steps one by one. ### Step 1: Convert Mixed Numbers to Improper Fractions 1. Convert \(4 \frac{5}{9}\): \[ 4 \frac{5}{9} = \frac{4 \times 9 + 5}{9} = \frac{36 + 5}{9} = \frac{41}{9} \] 2. Convert \(3 \frac{7}{12}\): \[ 3 \frac{7}{12} = \frac{3 \times 12 + 7}{12} = \frac{36 + 7}{12} = \frac{43}{12} \] 3. Convert \(-1 \frac{8}{27}\): \[ -1 \frac{8}{27} = \frac{-1 \times 27 - 8}{27} = \frac{-27 - 8}{27} = \frac{-35}{27} \] ### Step 2: Perform the Subtraction Next, we need to calculate: \[ \frac{41}{9} - \frac{43}{12} \] To perform this subtraction, find a common denominator. The least common multiple of 9 and 12 is 36. Convert \(\frac{41}{9}\) and \(\frac{43}{12}\) to have a denominator of 36: \[ \frac{41}{9} = \frac{41 \times 4}{9 \times 4} = \frac{164}{36} \] \[ \frac{43}{12} = \frac{43 \times 3}{12 \times 3} = \frac{129}{36} \] Now, subtract the two fractions: \[ \frac{164}{36} - \frac{129}{36} = \frac{164 - 129}{36} = \frac{35}{36} \] ### Step 3: Division by the Negative Fraction Now we need to divide \(\frac{35}{36}\) by \(\frac{-35}{27}\): \[ \frac{35}{36} \div \frac{-35}{27} = \frac{35}{36} \times \frac{-27}{35} \] The \(35\) cancels out: \[ = \frac{-27}{36} \] ### Step 4: Simplify the Result Now, simplify the fraction \(\frac{-27}{36}\): The GCD of 27 and 36 is 9: \[ \frac{-27 \div 9}{36 \div 9} = \frac{-3}{4} \] ### Final Result Thus, the result of the expression \((4 \frac{5}{9} - 3 \frac{7}{12}) : (-1 \frac{8}{27})\) is: \[ \boxed{-\frac{3}{4}} \]