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: Convert the repeating decimal 1.256 to a fraction. Let x = 1.256. This means x = 1.2565656... Multiply by 10 to move the non-repeating digit to the left of the decimal point: 10x = 12.565656... (*) Multiply by 1000 to move one full cycle of the repeating part to the left of the decimal point: 1000x = 1256.565656... (**) Subtract equation () from equation (*): 1000x - 10x = 1256.565656... - 12.565656... 990x = 1244 x = (1244)/(990) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2: x = (1244 ÷ 2)/(990 ÷ 2) = (622)/(495) Step 2: Convert the other decimals to fractions. 0.7 = (7)/(10) 0.15 = (15)/(100) = (3)/(20) Step 3: Substitute the fractions into the original expression. The expression is 1.256 + 0.7 - 0.15. Substituting the fractional forms: (622)/(495) + (7)/(10) - (3)/(20) Step 4: Find a common denominator for the fractions. The denominators are 495, 10, and 20. Prime factorization of the denominators: 495 = 3^2 × 5 × 11 10 = 2 × 5 20 = 2^2 × 5 The least common multiple (LCM) is 2^2 × 3^2 × 5 × 11 = 4 × 9 × 5 × 11 = 1980. Step 5: Convert each fraction to have the common denominator 1980. (622)/(495) = 622 × (19