1975 ÷ 7 = 282 R1
Alright, let's work through the division of 1975 by 7 step by step.

Step 1:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 7

Step 2:
7 goes into 19 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 14 from 19 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 7

Step 3:
7 goes into 57 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 28
Subtract 56 from 57 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 7

Step 4:
7 goes into 15 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 282
Subtract 14 from 15 to get 1.

The final result is 282 with a remainder of 1.