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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)55}\\\end{array}
Use the 1^{st} digit 5 from dividend 55
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)55}\\\end{array}
Since 5 is less than 11, use the next digit 5 from dividend 55 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)55}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55
\begin{array}{l}\phantom{11)}05\phantom{4}\\11\overline{)55}\\\phantom{11)}\underline{\phantom{}55\phantom{}}\\\phantom{11)99}0\\\end{array}
Find closest multiple of 11 to 55. We see that 5 \times 11 = 55 is the nearest. Now subtract 55 from 55 to get reminder 0. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }0
Since 0 is less than 11, stop the division. The reminder is 0. The topmost line 05 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.