Final answer:
The quotient of −4 1/2÷(−2 2/3) when simplified, is a positive 1 11/16. This calculation involves converting mixed numbers to improper fractions, multiplying by the reciprocal, and simplifying the resulting fraction.
Step-by-step explanation:
To calculate the quotient of −4 1/2÷(−2 2/3), you first need to convert the mixed numbers into improper fractions. The first step is to convert −4 1/2 into an improper fraction: −4 1/2 is the same as −9/2 because −4 equals −8/2, and adding the 1/2 gives −9/2. For −2 2/3, the process is similar: −2 2/3 is the same as −8/3 because −2 equals −6/3, and adding the 2/3 gives −8/3.
Now, you are left with the operation −9/2 ÷ −8/3. When dividing fractions, you multiply by the reciprocal of the second fraction. The reciprocal of −8/3 is −3/8. Therefore, the division turns into multiplication:
−9/2 × −3/8.
Applying the rules for multiplication of fractions, we multiply the numerators together and the denominators together. That yields (9×3)/(2×8) which simplifies to 27/16, and since we're dividing two numbers with the same sign, the quotient will be positive.
The final answer after simplification is 1 11/16 because 27/16 is the same as 1 with a remainder of 11, which gives us the mixed number 1 11/16.