Evaluate
\frac{156}{67}\approx 2.328358209
Factor
\frac{2 ^ {2} \cdot 3 \cdot 13}{67} = 2\frac{22}{67} = 2.328358208955224
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\begin{array}{l}\phantom{67)}\phantom{1}\\67\overline{)156}\\\end{array}
Use the 1^{st} digit 1 from dividend 156
\begin{array}{l}\phantom{67)}0\phantom{2}\\67\overline{)156}\\\end{array}
Since 1 is less than 67, use the next digit 5 from dividend 156 and add 0 to the quotient
\begin{array}{l}\phantom{67)}0\phantom{3}\\67\overline{)156}\\\end{array}
Use the 2^{nd} digit 5 from dividend 156
\begin{array}{l}\phantom{67)}00\phantom{4}\\67\overline{)156}\\\end{array}
Since 15 is less than 67, use the next digit 6 from dividend 156 and add 0 to the quotient
\begin{array}{l}\phantom{67)}00\phantom{5}\\67\overline{)156}\\\end{array}
Use the 3^{rd} digit 6 from dividend 156
\begin{array}{l}\phantom{67)}002\phantom{6}\\67\overline{)156}\\\phantom{67)}\underline{\phantom{}134\phantom{}}\\\phantom{67)9}22\\\end{array}
Find closest multiple of 67 to 156. We see that 2 \times 67 = 134 is the nearest. Now subtract 134 from 156 to get reminder 22. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }22
Since 22 is less than 67, stop the division. The reminder is 22. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}