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 3(3)/(4) to an improper fraction, multiply the whole number (3) by the denominator (4) and add the numerator (3). Keep the same denominator. 3(3)/(4) = ((3 × 4) + 3)/(4) = (12 + 3)/(4) = (15)/(4) To convert 2(2)/(3) to an improper fraction, multiply the whole number (2) by the denominator (3) and add the numerator (2). Keep the same denominator. 2(2)/(3) = ((2 × 3) + 2)/(3) = (6 + 2)/(3) = (8)/(3) The expression becomes: (15)/(4) + (8)/(3) Step 2: Find a common denominator for the fractions. The least common multiple (LCM) of 4 and 3 is 12. Convert each fraction to an equivalent fraction with a denominator of 12. For (15)/(4), multiply the numerator and denominator by 3: (15)/(4) = (15 × 3)/(4 × 3) = (45)/(12) For (8)/(3), multiply the numerator and denominator by 4: (8)/(3) = (8 × 4)/(3 × 4) = (32)/(12) The expression becomes: (45)/(12) + (32)/(12) Step 3: Add the fractions. Now that the fractions have a common denominator, add their numerators. (45)/(12) + (32)/(12) = (45 + 32)/(12) = (77)/(12) Step 4: Convert the improper fraction back to a mixed number. Divide the numerator (77) by the denominator (12). 77 ÷ 12 = 6 with a remainder of 5 So, (77)/(12) can be written as 6(5)/(12). The final answer is 6(5)/(12). That's 2 down. 3 left today — send the next one.