Represent the mixed number as N a/b where N is the whole number part and a over b is the fraction.
Method 1
Write down N and follow it by a decimal point.
Now you need to divide b into a, but because a is smaller than b you need to write a, a decimal point, and as many zeroes as you wish for accuracy. Some decimals terminate (divide exactly) and some recur (a pattern repeats indefinitely). Example: a=3 and b=4 so we have 3/4. Divide b into 3.0000... Treat 3.0 as 30 and divide by 4, putting the answer immediately after the decimal point. So we have .7 and 2 over making 20 with the next zero. Now divide 4 into 20 and write the result after the 7: .75. This is an exact division so we don't need to go any further. Let's say N was 5 so the mixed number is 5 3/4. We've already written N as 5. so now we continue after the decimal point with what we just calculated giving us 5.75.
Another example: 7 5/6.
We write 7. first.
Divide 6 into 5.0000... and we get .8333. This is a recurring decimal. We keep getting the same carryover.
Now we attach the whole number part to get 7.83333...
Another example: 2 1/16.
We write 2. first.
But be careful in the next part: 16 divided into 1.0000... 16 doesn't go into 10 so we write .0 as our first number. Then we divide 16 into 100. This is 6 remainder 4. So we have .06. 16 into 40 goes 2 remainder 8. That gives us .062. Finally 16 into 80 is exactly 5 so we have .0625. Attach this to the whole number: 2.0625.
Method 2
For N a/b we make the improper fraction b*N+a over b, then divide by b.
Example: 2 1/16: 16*2+1=33. So we divide 33.000.... by 16. We end up with 2.0625.
Example: 7 5/6: divide 6*7+5=47 by 6. We end up with 7.83333...