870 ÷ 77 
Our goal is to divide 870 by 77.

Going ahead to step 1:
77 goes into 8 0 times with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Fetch the next digit (7) from the dividend, attach it to 8 and continue: 87 / 77

On to step 2:
The number 77 fits into 87 1 times, leaving a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 77 from 87 to get 10.
Take the next digit (0) from the dividend and append it to 10, then repeat: 100 / 77

Moving on to step 3:
If we divide 100 by 77, we get 1 and a remainder of 23.
Use 1 as the next digit of our solution. 
Result so far: 11.0
If we take 77 away from 100, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

On to step 4:
230 divided by 77 is 2 with a remainder of 76.
Use 2 as the next digit of our solution. 
Result so far: 11.2
Subtract 154 from 230 to get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Advancing to step 5:
The number 77 fits into 760 9 times, leaving a remainder of 67.
The next digit of our result is 9. 
Result so far: 11.29
If we take 693 away from 760, we end up with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Let's proceed to step 6:
77 goes into 670 8 times with a remainder of 54.
The next digit of our result is 8. 
Result so far: 11.298
If we take 616 away from 670, we end up with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Moving on to step 7:
540 divided by 77 is 7 with a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 11.2987
Deduct 539 from 540 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 8:
If we divide 10 by 77, we get 0 and a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 11.2987
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 9:
77 goes into 100 1 times with a remainder of 23.
Write down 1 as next digit of the result. 
Result so far: 11.298701
The remainder is 23 after subtracting 77 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

On to step 10:
When dividing 230 by 77, we get 2 with a remainder of 76.
The next digit of our result is 2. 
Result so far: 11.2987012
Deduct 154 from 230 and we're left with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

On to step 11:
77 goes into 760 9 times with a remainder of 67.
Write down 9 as next digit of the result. 
Result so far: 11.29870129
If we subtract 693 from 760, we get 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

The final result is 11.29870129 with a remainder of 6.7e-08.