Evaluate
6
Factor
2\times 3
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)138}\\\end{array}
Use the 1^{st} digit 1 from dividend 138
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)138}\\\end{array}
Since 1 is less than 23, use the next digit 3 from dividend 138 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)138}\\\end{array}
Use the 2^{nd} digit 3 from dividend 138
\begin{array}{l}\phantom{23)}00\phantom{4}\\23\overline{)138}\\\end{array}
Since 13 is less than 23, use the next digit 8 from dividend 138 and add 0 to the quotient
\begin{array}{l}\phantom{23)}00\phantom{5}\\23\overline{)138}\\\end{array}
Use the 3^{rd} digit 8 from dividend 138
\begin{array}{l}\phantom{23)}006\phantom{6}\\23\overline{)138}\\\phantom{23)}\underline{\phantom{}138\phantom{}}\\\phantom{23)999}0\\\end{array}
Find closest multiple of 23 to 138. We see that 6 \times 23 = 138 is the nearest. Now subtract 138 from 138 to get reminder 0. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }0
Since 0 is less than 23, stop the division. The reminder is 0. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}