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: Identify the total length of the rope and the lengths of the pieces cut off. Total length of the rope = 11 m. Length of the first piece cut off = 3 (2)/(3) m. Length of the second piece cut off = 3 (1)/(10) m. Step 2: Convert the mixed numbers to improper fractions. 3 (2)/(3) = ((3 × 3) + 2)/(3) = (9 + 2)/(3) = (11)/(3) m 3 (1)/(10) = ((3 × 10) + 1)/(10) = (30 + 1)/(10) = (31)/(10) m Step 3: Calculate the total length of the pieces cut off. To add the fractions, find a common denominator, which is 3 × 10 = 30. Total cut length = (11)/(3) + (31)/(10) Total cut length = (11 × 10)/(3 × 10) + (31 × 3)/(10 × 3) Total cut length = (110)/(30) + (93)/(30) Total cut length = (110 + 93)/(30) = (203)/(30) m Step 4: Calculate the length of the remaining rope. Subtract the total cut length from the original total length of the rope. Remaining length = 11 - (203)/(30) Convert 11 to a fraction with a denominator of 30: 11 = (11 × 30)/(30) = (330)/(30) Remaining length = (330)/(30) - (203)/(30) Remaining length = (330 - 203)/(30) = (127)/(30) m Step 5: Convert the improper fraction to a mixed number. (127)/(30) = 4 (7)/(30) m The length of the remaining rope is 4 (7)/(30) m.