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
The simplified ratio is 42 : 80 : 45. Here's how to simplify the ratio: 1. Convert the decimal to a fraction: 0.35 = 35/100 = 7/20 2. Identify all fractions in the ratio: 7/20, 2/3, 3/8 3. Find the Least Common Multiple (LCM) of the denominators (20, 3, 8): Prime factorization of 20 = 2² × 5 Prime factorization of 3 = 3 Prime factorization of 8 = 2³ LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120 4. Convert each fraction to an equivalent fraction with the LCM as the denominator: 7/20 = (7 × 6) / (20 × 6) = 42/120 2/3 = (2 × 40) / (3 × 40) = 80/120 3/8 = (3 × 15) / (8 × 15) = 45/120 5. Write the ratio using the new fractions and then remove the common denominator: 42/120 : 80/120 : 45/120 Multiply all parts by 120 to get integer ratios: 42 : 80 : 45 6. Check if the integer ratio can be further simplified: The numbers 42, 80, and 45 do not share any common factors other than 1. 42 = 2 × 3 × 7 80 = 2⁴ × 5 45 = 3² × 5 Since there are no common prime factors across all three numbers, the ratio is in its simplest form.