Evaluate
38
Factor
2\times 19
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)532}\\\end{array}
Use the 1^{st} digit 5 from dividend 532
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)532}\\\end{array}
Since 5 is less than 14, use the next digit 3 from dividend 532 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)532}\\\end{array}
Use the 2^{nd} digit 3 from dividend 532
\begin{array}{l}\phantom{14)}03\phantom{4}\\14\overline{)532}\\\phantom{14)}\underline{\phantom{}42\phantom{9}}\\\phantom{14)}11\\\end{array}
Find closest multiple of 14 to 53. We see that 3 \times 14 = 42 is the nearest. Now subtract 42 from 53 to get reminder 11. Add 3 to quotient.
\begin{array}{l}\phantom{14)}03\phantom{5}\\14\overline{)532}\\\phantom{14)}\underline{\phantom{}42\phantom{9}}\\\phantom{14)}112\\\end{array}
Use the 3^{rd} digit 2 from dividend 532
\begin{array}{l}\phantom{14)}038\phantom{6}\\14\overline{)532}\\\phantom{14)}\underline{\phantom{}42\phantom{9}}\\\phantom{14)}112\\\phantom{14)}\underline{\phantom{}112\phantom{}}\\\phantom{14)999}0\\\end{array}
Find closest multiple of 14 to 112. We see that 8 \times 14 = 112 is the nearest. Now subtract 112 from 112 to get reminder 0. Add 8 to quotient.
\text{Quotient: }38 \text{Reminder: }0
Since 0 is less than 14, stop the division. The reminder is 0. The topmost line 038 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 38.
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}