simplify the ratio 0.35, 2\3,3\8

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ScanSolve AI Tutor · Accepted 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.

Simplify the ratio 0.35, 2\3,3\8

Step-by-step solution

Convert the decimal to a fraction

Identify all fractions in the ratio

Find the Least Common Multiple (LCM) of the denominators (20, 3, 8)

Convert each fraction to an equivalent fraction with the LCM as the denominator

Write the ratio using the new fractions and then remove the common denominator

Check if the integer ratio can be further simplified

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