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: Perform the multiplication. (4)/(5) × (2)/(3) = (4 × 2)/(5 × 3) = (8)/(15) Step 2: Perform the division. To divide by a fraction, multiply by its reciprocal. (2)/(10) ÷ (3)/(5) = (2)/(10) × (5)/(3) Multiply the numerators and the denominators. (2 × 5)/(10 × 3) = (10)/(30) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 10. (10 ÷ 10)/(30 ÷ 10) = (1)/(3) Step 3: Subtract the result of Step 2 from the result of Step 1. (8)/(15) - (1)/(3) To subtract these fractions, find a common denominator. The least common multiple of 15 and 3 is 15. Convert (1)/(3) to an equivalent fraction with a denominator of 15. (1)/(3) = (1 × 5)/(3 × 5) = (5)/(15) Now perform the subtraction. (8)/(15) - (5)/(15) = (8 - 5)/(15) = (3)/(15) Step 4: Simplify the final fraction. Divide the numerator and denominator by their greatest common divisor, which is 3. (3 ÷ 3)/(15 ÷ 3) = (1)/(5) The simplified expression is (1)/(5).