Final answer:
The expression 5 7/8 - (3 1/2 + 1 1/4) evaluates to 1 1/8 after combining the numbers in the parentheses, converting to improper fractions, finding a common denominator, subtracting the fractions, and finally converting back to a mixed number.
Step-by-step explanation:
To evaluate the expression 5 7/8 - (3 1/2 + 1 1/4), first combine the numbers in parentheses.
- Add 3 1/2 and 1 1/4 together:
3 1/2 + 1 1/4 = 3.5 + 1.25 = 4.75 - Next, convert 5 7/8 to an improper fraction:
5 7/8 = (5 × 8 + 7) / 8 = (40 + 7) / 8 = 47/8 - Now convert 4 3/4 (which is the same as 4.75) to an improper fraction:
4 3/4 = (4 × 4 + 3) / 4 = (16 + 3) / 4 = 19/4 - Next, find a common denominator and subtract the two fractions:
47/8 - 19/4 = 47/8 - (19/4 × 2/2) = 47/8 - 38/8 = (47 - 38) / 8 = 9/8 - Lastly, reduce the fraction 9/8 to a mixed number:
9/8 = 1 1/8
Thus, 5 7/8 - (3 1/2 + 1 1/4) equals 1 1/8.