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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You're on a roll — here are the solutions for the fraction multiplication problems: Problem 1: (12)/(4) × (16)/(12) × (4)/(8) Step 1: Simplify the fractions by cross-cancellation. (12)/(4) × (16)/(12) × (4)/(8) Cancel 12 (numerator of the first fraction) and 12 (denominator of the second fraction): 12 ÷ 12 = 1. The expression becomes: (1)/(4) × (16)/(1) × (4)/(8) Cancel 16 (numerator of the second fraction) and 4 (denominator of the first fraction): 16 ÷ 4 = 4, 4 ÷ 4 = 1. The expression becomes: (1)/(1) × (4)/(1) × (4)/(8) Cancel 4 (numerator of the second fraction) and 8 (denominator of the third fraction): 4 ÷ 4 = 1, 8 ÷ 4 = 2. The expression becomes: (1)/(1) × (1)/(1) × (4)/(2) Simplify (4)/(2) to (2)/(1). (1)/(1) × (1)/(1) × (2)/(1) Step 2: Multiply the remaining numerators and denominators. (1 × 1 × 2)/(1 × 1 × 1) = (2)/(1) = 2 The final answer is 2. Problem 2: (12)/(6) × (15)/(12) × (12)/(4) Step 1: Simplify the fractions by cross-cancellation. (12)/(6) × (15)/(12) × (12)/(4) Cancel 12 (numerator of the first fraction) and 12 (denominator of the second fraction): 12 ÷ 12 = 1. The expression becomes: (1)/(6) × (15)/(1) × (12)/(4) Cancel 15 (numerator of the second fraction) and 6 (denominator of the first fraction) by dividing by 3: 15 ÷ 3 = 5, 6 ÷ 3 = 2. The expression becomes: (1)/(2) × (5)/(1) × (12)/(4) Cancel 12 (numerator of the third fraction) and 4 (denominator of the third fraction): 12 ÷ 4 = 3, 4 ÷ 4 = 1. The expression becomes: (1)/(2) × (5)/(1) × (3)/(1) Step 2: Multiply the remaining numerators and denominators. (1 × 5 × 3)/(2 × 1 × 1) = (15)/(2) The final answer is (15)/(2). What's next?