Solve the following mathematical expression: (0.9:[ (0.125 - 1/9) + (0.5 + 1/4) ] : [1 7/15 - 1 1/15] - (0.5 + 3/4) : 13) - 18 - 1/5

Solution:

• Convert all numbers to fractions:
• 0.9 = 9/10
• 0.125 = 1/8
• 0.5 = 1/2
• 1 7/15 = 22/15
• 1 1/15 = 16/15
• 3/4
• 1/5
• Calculate the expression step-by-step:
• (0.125 - 1/9) = (1/8 - 1/9) = (9/72 - 8/72) = 1/72
• (0.5 + 1/4) = (1/2 + 1/4) = (2/4 + 1/4) = 3/4
• [ (1/72) + (3/4) ] = [1/72 + 54/72] = 55/72
• [1 7/15 - 1 1/15] = [22/15 - 16/15] = 6/15 = 2/5
• (0.5 + 3/4) = (1/2 + 3/4) = (2/4 + 3/4) = 5/4
• 0.9 : [55/72] = 9/10 * 72/55 = (9 * 36) / (5 * 55) = 324/275
• (324/275) : (2/5) = 324/275 * 5/2 = (162 * 1) / (55 * 1) = 162/55
• (5/4) : 13 = 5/4 * 1/13 = 5/52
• (162/55) - (5/52) = (162 * 52 - 5 * 55) / (55 * 52) = (8424 - 275) / 2860 = 8149/2860
• 18 + 1/5 = 90/5 + 1/5 = 91/5
• (8149/2860) - (91/5) = (8149 - 91 * 572) / 2860 = (8149 - 52052) / 2860 = -43903/2860

Ответ: -43903/2860