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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)55}\\\end{array}
Use the 1^{st} digit 5 from dividend 55
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)55}\\\end{array}
Since 5 is less than 45, use the next digit 5 from dividend 55 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)55}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)55}\\\phantom{45)}\underline{\phantom{}45\phantom{}}\\\phantom{45)}10\\\end{array}
Find closest multiple of 45 to 55. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 55 to get reminder 10. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }10
Since 10 is less than 45, stop the division. The reminder is 10. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.