Evaluate
\frac{186}{5}=37.2
Factor
\frac{2 \cdot 3 \cdot 31}{5} = 37\frac{1}{5} = 37.2
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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)37200}\\\end{array}
Use the 1^{st} digit 3 from dividend 37200
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)37200}\\\end{array}
Since 3 is less than 1000, use the next digit 7 from dividend 37200 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)37200}\\\end{array}
Use the 2^{nd} digit 7 from dividend 37200
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)37200}\\\end{array}
Since 37 is less than 1000, use the next digit 2 from dividend 37200 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)37200}\\\end{array}
Use the 3^{rd} digit 2 from dividend 37200
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)37200}\\\end{array}
Since 372 is less than 1000, use the next digit 0 from dividend 37200 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)37200}\\\end{array}
Use the 4^{th} digit 0 from dividend 37200
\begin{array}{l}\phantom{1000)}0003\phantom{8}\\1000\overline{)37200}\\\phantom{1000)}\underline{\phantom{}3000\phantom{9}}\\\phantom{1000)9}720\\\end{array}
Find closest multiple of 1000 to 3720. We see that 3 \times 1000 = 3000 is the nearest. Now subtract 3000 from 3720 to get reminder 720. Add 3 to quotient.
\begin{array}{l}\phantom{1000)}0003\phantom{9}\\1000\overline{)37200}\\\phantom{1000)}\underline{\phantom{}3000\phantom{9}}\\\phantom{1000)9}7200\\\end{array}
Use the 5^{th} digit 0 from dividend 37200
\begin{array}{l}\phantom{1000)}00037\phantom{10}\\1000\overline{)37200}\\\phantom{1000)}\underline{\phantom{}3000\phantom{9}}\\\phantom{1000)9}7200\\\phantom{1000)}\underline{\phantom{9}7000\phantom{}}\\\phantom{1000)99}200\\\end{array}
Find closest multiple of 1000 to 7200. We see that 7 \times 1000 = 7000 is the nearest. Now subtract 7000 from 7200 to get reminder 200. Add 7 to quotient.
\text{Quotient: }37 \text{Reminder: }200
Since 200 is less than 1000, stop the division. The reminder is 200. The topmost line 00037 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 37.
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}