Evaluate
\frac{42}{5}=8.4
Factor
\frac{2 \cdot 3 \cdot 7}{5} = 8\frac{2}{5} = 8.4
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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)8400}\\\end{array}
Use the 1^{st} digit 8 from dividend 8400
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)8400}\\\end{array}
Since 8 is less than 1000, use the next digit 4 from dividend 8400 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)8400}\\\end{array}
Use the 2^{nd} digit 4 from dividend 8400
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)8400}\\\end{array}
Since 84 is less than 1000, use the next digit 0 from dividend 8400 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)8400}\\\end{array}
Use the 3^{rd} digit 0 from dividend 8400
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)8400}\\\end{array}
Since 840 is less than 1000, use the next digit 0 from dividend 8400 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)8400}\\\end{array}
Use the 4^{th} digit 0 from dividend 8400
\begin{array}{l}\phantom{1000)}0008\phantom{8}\\1000\overline{)8400}\\\phantom{1000)}\underline{\phantom{}8000\phantom{}}\\\phantom{1000)9}400\\\end{array}
Find closest multiple of 1000 to 8400. We see that 8 \times 1000 = 8000 is the nearest. Now subtract 8000 from 8400 to get reminder 400. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }400
Since 400 is less than 1000, stop the division. The reminder is 400. The topmost line 0008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}