Evaluate
\frac{277}{20}=13.85
Factor
\frac{277}{2 ^ {2} \cdot 5} = 13\frac{17}{20} = 13.85
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)554}\\\end{array}
Use the 1^{st} digit 5 from dividend 554
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)554}\\\end{array}
Since 5 is less than 40, use the next digit 5 from dividend 554 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)554}\\\end{array}
Use the 2^{nd} digit 5 from dividend 554
\begin{array}{l}\phantom{40)}01\phantom{4}\\40\overline{)554}\\\phantom{40)}\underline{\phantom{}40\phantom{9}}\\\phantom{40)}15\\\end{array}
Find closest multiple of 40 to 55. We see that 1 \times 40 = 40 is the nearest. Now subtract 40 from 55 to get reminder 15. Add 1 to quotient.
\begin{array}{l}\phantom{40)}01\phantom{5}\\40\overline{)554}\\\phantom{40)}\underline{\phantom{}40\phantom{9}}\\\phantom{40)}154\\\end{array}
Use the 3^{rd} digit 4 from dividend 554
\begin{array}{l}\phantom{40)}013\phantom{6}\\40\overline{)554}\\\phantom{40)}\underline{\phantom{}40\phantom{9}}\\\phantom{40)}154\\\phantom{40)}\underline{\phantom{}120\phantom{}}\\\phantom{40)9}34\\\end{array}
Find closest multiple of 40 to 154. We see that 3 \times 40 = 120 is the nearest. Now subtract 120 from 154 to get reminder 34. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }34
Since 34 is less than 40, stop the division. The reminder is 34. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}