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.
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Problem 1 Add (1)/(2) + (3)/(8) + (1)/(3). Step 1: Find LCD of denominators 2, 8, 3. LCD = 2^3 × 3 = 24 Step 2: Convert (1)/(2). (1)/(2) = (1 × 12)/(2 × 12) = (12)/(24) Step 3: Convert (3)/(8). (3)/(8) = (3 × 3)/(8 × 3) = (9)/(24) Step 4: Convert (1)/(3). (1)/(3) = (1 × 8)/(3 × 8) = (8)/(24) Step 5: Add the fractions. (12)/(24) + (9)/(24) + (8)/(24) = (12 + 9 + 8)/(24) = (29)/(24) Step 6: (29)/(24) is in simplest form (29 is prime). Final answer: (29)/(24) Problem 2 Add (7)/(5) + (3)/(2). Step 1: Find LCD of denominators 5, 2. LCD = 5 × 2 = 10 Step 2: Convert (7)/(5). (7)/(5) = (7 × 2)/(5 × 2) = (14)/(10) Step 3: Convert (3)/(2). (3)/(2) = (3 × 5)/(2 × 5) = (15)/(10) Step 4: Add the fractions. (14)/(10) + (15)/(10) = (14 + 15)/(10) = (29)/(10) Step 5: (29)/(10) is in simplest form. Final answer: (29)/(10) Problem 3 Multiply (2)/(2) × (1)/(5). Step 1: Multiply numerators and denominators. (2)/(2) × (1)/(5) = (2 × 1)/(2 × 5) = (2)/(10) Step 2: Simplify (2)/(10). (2 ÷ 2)/(10 ÷ 2) = (1)/(5) Final answer: (1)/(5) Problem 4 Multiply 3 × (3)/(5). Step 1: Write 3 as (3)/(1). 3 × (3)/(5) = (3)/(1) × (3)/(5) Step 2: Multiply numerators and denominators. (3 × 3)/(1 × 5) = (9)/(5) Step 3: (9)/(5) is in simplest form. Final answer: (9)/(5)