97 1/6 + 11/39 - 6 8/13 - 10/21 * (9/16 + 3,075 * 0,5) : 1/83=

1) 3,075*0,5=1,5375

2) 9/16+1,5375=0,5625+1,5375=2,1

3) 10/21*2,1=10/21*21/10=1

4) 1:1/83=83

5) 97 1/6+11/39-6 8/13=97 13/78+22/78-6 48/78=97 35/78-6 48/78=

=96 113/78-6 48/76=90 65/78=90 5/6

6) 90 5/6-83=7 5/6

97 1/6 + 11/39 - 6 8/13 - 10/21 * (9/16 + 3,075 * 0,5) : 1/83 = 7 5/6

4) 1 : 1/83=1*83=83

5) 97 1/6 + 11/39 = 583/6 + 11/39 = (583 * 13 + 11 * 2) / 78 = 7579/78 + 22/78 = 7601/78 = 97 35/78

6) 97 35/78 - 6 8/13 = 7601/78 - 86/13 = (7601 * 1 - 86 * 6) / 78 = 7601/78 - 516/78 = 7085/78 = 545/6 = 90 5/6

7) 90 5/6 - 83 = 545/6 - 83 = (545 * 1 - 83 * 6) / 6 = 545/6 - 498/6 = 47/6 = 7 5/6