This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Convert the mixed numbers to improper fractions. To convert a mixed number a(b)/(c) to an improper fraction, use the formula ((a × c) + b)/(c). For 7(1)/(8): 7(1)/(8) = ((7 × 8) + 1)/(8) = (56 + 1)/(8) = (57)/(8) For 5(4)/(5): 5(4)/(5) = ((5 × 5) + 4)/(5) = (25 + 4)/(5) = (29)/(5) Step 2: Find a common denominator for the fractions. The denominators are 8 and 5. The least common multiple (LCM) of 8 and 5 is 8 × 5 = 40. Convert (57)/(8) to an equivalent fraction with a denominator of 40: (57)/(8) = (57 × 5)/(8 × 5) = (285)/(40) Convert (29)/(5) to an equivalent fraction with a denominator of 40: (29)/(5) = (29 × 8)/(5 × 8) = (232)/(40) Step 3: Subtract the fractions. Now subtract the fractions with the common denominator: (285)/(40) - (232)/(40) = (285 - 232)/(40) = (53)/(40) Step 4: Convert the improper fraction back to a mixed number. Divide the numerator (53) by the denominator (40). 53 ÷ 40 = 1 with a remainder of 53 - (1 × 40) = 13. The quotient (1) is the whole number part, and the remainder (13) is the new numerator over the original denominator (40). (53)/(40) = 1(13)/(40) The final answer is 1(13)/(40).