Evaluate
\frac{275}{14}\approx 19.642857143
Factor
\frac{5 ^ {2} \cdot 11}{2 \cdot 7} = 19\frac{9}{14} = 19.642857142857142
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)275}\\\end{array}
Use the 1^{st} digit 2 from dividend 275
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)275}\\\end{array}
Since 2 is less than 14, use the next digit 7 from dividend 275 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)275}\\\end{array}
Use the 2^{nd} digit 7 from dividend 275
\begin{array}{l}\phantom{14)}01\phantom{4}\\14\overline{)275}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)}13\\\end{array}
Find closest multiple of 14 to 27. We see that 1 \times 14 = 14 is the nearest. Now subtract 14 from 27 to get reminder 13. Add 1 to quotient.
\begin{array}{l}\phantom{14)}01\phantom{5}\\14\overline{)275}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)}135\\\end{array}
Use the 3^{rd} digit 5 from dividend 275
\begin{array}{l}\phantom{14)}019\phantom{6}\\14\overline{)275}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)}135\\\phantom{14)}\underline{\phantom{}126\phantom{}}\\\phantom{14)99}9\\\end{array}
Find closest multiple of 14 to 135. We see that 9 \times 14 = 126 is the nearest. Now subtract 126 from 135 to get reminder 9. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }9
Since 9 is less than 14, stop the division. The reminder is 9. The topmost line 019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.
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}