Final answer:
Evaluating the expression -4 1/2 - (-23/8) involves converting mixed numbers to improper fractions, finding a common denominator, and performing the addition or subtraction of fractions correctly. The answer is -1 5/8, which does not match any of the provided options.
Step-by-step explanation:
To evaluate the expression -4 1/2 - (-23/8), we need to convert the mixed number to an improper fraction and then perform the subtraction with due attention to the signs involved. First, we convert -4 1/2 to an improper fraction:
- Multiply the denominator of the fractional part by the whole number: 2 * 4 = 8.
- Add the numerator of the fractional part: 8 + 1 = 9.
- Since the whole number is negative, the resulting fraction is -9/2.
The expression now reads -9/2 - (-23/8). Remembering that subtracting a negative is the same as adding a positive, we have:
To add these fractions, find a common denominator. The least common denominator of 2 and 8 is 8. We convert -9/2 to a fraction with a denominator of 8:
- Multiply numerator and denominator by 4: -9/2 * 4/4 = -36/8.
Now we can add the two fractions:
- -36/8 + 23/8 = (-36 + 23)/8
- -13/8
Since -13/8 cannot be simplified further, we convert it back into a mixed number:
- Divide the numerator by the denominator to get the whole number part: -13 ÷ 8 = -1 with a remainder of 5.
- The remainder is the new numerator, so we have -1 5/8.
So the correct answer is -1 5/8, which actually does not match any of the provided options (A) -4 5/8, (B) -3 1/4, (C) -5 3/8, (D) -2 7/8. It is possible there was an error in the provided options or in the question.