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
To work out the expression without using a calculator, we will simplify the numerator and the denominator separately. The expression is: (4)/(5) + (7)/(8)1 + ((1)/(4) × (5)/(18)) Step 1: Simplify the numerator. Numerator = (4)/(5) + (7)/(8) To add these fractions, find a common denominator, which is 40. (4)/(5) = (4 × 8)/(5 × 8) = (32)/(40) (7)/(8) = (7 × 5)/(8 × 5) = (35)/(40) Now, add the fractions: Numerator = (32)/(40) + (35)/(40) = (32+35)/(40) = (67)/(40) Step 2: Simplify the term in the parenthesis in the denominator. (1)/(4) × (5)/(18) = (1 × 5)/(4 × 18) = (5)/(72) Step 3: Simplify the denominator. Denominator = 1 + (5)/(72) Convert 1 to a fraction with denominator 72: 1 = (72)/(72) Now, add the fractions: Denominator = (72)/(72) + (5)/(72) = (72+5)/(72) = (77)/(72) Step 4: Divide the simplified numerator by the simplified denominator. NumeratorDenominator = (67)/(40)(77)/(72) To divide by a fraction, multiply by its reciprocal: (67)/(40) × (72)/(77) We can simplify by dividing 40 and 72 by their greatest common divisor, which is 8: 40 ÷ 8 = 5 72 ÷ 8 = 9 So the expression becomes: (67)/(5) × (9)/(77) Now, multiply the numerators and the denominators: Result = (67 × 9)/(5 × 77) 67 × 9 = 603 5 × 77 = 385 Therefore, the final answer is: (603)/(385) This fraction cannot be simplified further as the prime factors of 603 are 3^2 × 67 and the prime factors of 385 are 5 × 7 × 11. The final answer is (603)/(385). That's 2 down. 3 left today — send the next one.