Evaluate
\frac{233}{70}\approx 3.328571429
Factor
\frac{233}{2 \cdot 5 \cdot 7} = 3\frac{23}{70} = 3.3285714285714287
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)233}\\\end{array}
Use the 1^{st} digit 2 from dividend 233
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)233}\\\end{array}
Since 2 is less than 70, use the next digit 3 from dividend 233 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)233}\\\end{array}
Use the 2^{nd} digit 3 from dividend 233
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)233}\\\end{array}
Since 23 is less than 70, use the next digit 3 from dividend 233 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)233}\\\end{array}
Use the 3^{rd} digit 3 from dividend 233
\begin{array}{l}\phantom{70)}003\phantom{6}\\70\overline{)233}\\\phantom{70)}\underline{\phantom{}210\phantom{}}\\\phantom{70)9}23\\\end{array}
Find closest multiple of 70 to 233. We see that 3 \times 70 = 210 is the nearest. Now subtract 210 from 233 to get reminder 23. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }23
Since 23 is less than 70, stop the division. The reminder is 23. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}