Evaluate
\frac{712}{5}=142.4
Factor
\frac{2 ^ {3} \cdot 89}{5} = 142\frac{2}{5} = 142.4
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)5696}\\\end{array}
Use the 1^{st} digit 5 from dividend 5696
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)5696}\\\end{array}
Since 5 is less than 40, use the next digit 6 from dividend 5696 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)5696}\\\end{array}
Use the 2^{nd} digit 6 from dividend 5696
\begin{array}{l}\phantom{40)}01\phantom{4}\\40\overline{)5696}\\\phantom{40)}\underline{\phantom{}40\phantom{99}}\\\phantom{40)}16\\\end{array}
Find closest multiple of 40 to 56. We see that 1 \times 40 = 40 is the nearest. Now subtract 40 from 56 to get reminder 16. Add 1 to quotient.
\begin{array}{l}\phantom{40)}01\phantom{5}\\40\overline{)5696}\\\phantom{40)}\underline{\phantom{}40\phantom{99}}\\\phantom{40)}169\\\end{array}
Use the 3^{rd} digit 9 from dividend 5696
\begin{array}{l}\phantom{40)}014\phantom{6}\\40\overline{)5696}\\\phantom{40)}\underline{\phantom{}40\phantom{99}}\\\phantom{40)}169\\\phantom{40)}\underline{\phantom{}160\phantom{9}}\\\phantom{40)99}9\\\end{array}
Find closest multiple of 40 to 169. We see that 4 \times 40 = 160 is the nearest. Now subtract 160 from 169 to get reminder 9. Add 4 to quotient.
\begin{array}{l}\phantom{40)}014\phantom{7}\\40\overline{)5696}\\\phantom{40)}\underline{\phantom{}40\phantom{99}}\\\phantom{40)}169\\\phantom{40)}\underline{\phantom{}160\phantom{9}}\\\phantom{40)99}96\\\end{array}
Use the 4^{th} digit 6 from dividend 5696
\begin{array}{l}\phantom{40)}0142\phantom{8}\\40\overline{)5696}\\\phantom{40)}\underline{\phantom{}40\phantom{99}}\\\phantom{40)}169\\\phantom{40)}\underline{\phantom{}160\phantom{9}}\\\phantom{40)99}96\\\phantom{40)}\underline{\phantom{99}80\phantom{}}\\\phantom{40)99}16\\\end{array}
Find closest multiple of 40 to 96. We see that 2 \times 40 = 80 is the nearest. Now subtract 80 from 96 to get reminder 16. Add 2 to quotient.
\text{Quotient: }142 \text{Reminder: }16
Since 16 is less than 40, stop the division. The reminder is 16. The topmost line 0142 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 142.
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}