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\begin{array}{l}\phantom{44)}\phantom{1}\\44\overline{)55}\\\end{array}
Use the 1^{st} digit 5 from dividend 55
\begin{array}{l}\phantom{44)}0\phantom{2}\\44\overline{)55}\\\end{array}
Since 5 is less than 44, use the next digit 5 from dividend 55 and add 0 to the quotient
\begin{array}{l}\phantom{44)}0\phantom{3}\\44\overline{)55}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55
\begin{array}{l}\phantom{44)}01\phantom{4}\\44\overline{)55}\\\phantom{44)}\underline{\phantom{}44\phantom{}}\\\phantom{44)}11\\\end{array}
Find closest multiple of 44 to 55. We see that 1 \times 44 = 44 is the nearest. Now subtract 44 from 55 to get reminder 11. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }11
Since 11 is less than 44, stop the division. The reminder is 11. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.