hi greg ,

didn’t understand the solution for this problem.

0.63636363…+0.11111111

write in simplest form of fraction

Consider x = 0.6363… & y = 0.111…

Multiplying x by 100 gives 100x = 63.6363… We multiply by 100 because there are two digits after the decimal, which are repeated in a periodic fashion. To eliminate the recurring part, we need to multiply both sides by 10^(the number of digits in one period)

Subtracting the equations of variable x, we get, 100x - x = 63.6363… - 0.6363…, which gives us 99x = 63. Therefore x becomes 63/99 or 7/11.

Similarly, for y = 0.111…, multiply both sides by 10. This subsequently gives us 10y = 1.111… Subtracting from both sides gives us 9y = 1 or y = 1/9. (We multiplied by 10 because there is only one digit in the repeating cycle)

After conversion from recurring decimal to regular fraction, we can add x & y using traditional addition methods.

x + y = 7/11 + 1/9 = ((7*9)+(1*11))/99 = (63+11)/99 = 74/99

Hope this helps.