a) Multiply by 100 to get 123.7777... This separates the recurring part of the decimal from the rest of the number. Now we take the recurring digit(s). There’s only, that’s 7, so we divide by as many 9s, so we need only one to give us 7/9 as a fraction. What we have now is 123 and 7/9. Convert to an improper fraction: 1114/9 (1114=9×123+7). But remember we multiplied by 100 so we now have to divide by that: 1114/900=557/450. That is the fraction in its most reduced form.
b) I guess that 8 should be 7 to make the recurring part 745. Follow the rules in (a) and we get 745/999 as the fraction. This doesn’t reduce further so work out the improper fraction: 3+745/999=3742/999.
c) Multiply by 100: 823.2727.... 27/99=3/11. So we have 823+3/11=9056/11. Now divide by 100: 9056/1100=2264/275.
d) Multiply by 10: 32.3838.... 38/99 is the fraction. So 32+38/99 is 3206/99. Now divide by 10: 3206/990=1603/495.