Evaluate
\frac{40}{3}\approx 13.333333333
Factor
\frac{2 ^ {3} \cdot 5}{3} = 13\frac{1}{3} = 13.333333333333334
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)400}\\\end{array}
Use the 1^{st} digit 4 from dividend 400
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)400}\\\end{array}
Since 4 is less than 30, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 400
\begin{array}{l}\phantom{30)}01\phantom{4}\\30\overline{)400}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}10\\\end{array}
Find closest multiple of 30 to 40. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 40 to get reminder 10. Add 1 to quotient.
\begin{array}{l}\phantom{30)}01\phantom{5}\\30\overline{)400}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}100\\\end{array}
Use the 3^{rd} digit 0 from dividend 400
\begin{array}{l}\phantom{30)}013\phantom{6}\\30\overline{)400}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}100\\\phantom{30)}\underline{\phantom{9}90\phantom{}}\\\phantom{30)9}10\\\end{array}
Find closest multiple of 30 to 100. We see that 3 \times 30 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }10
Since 10 is less than 30, stop the division. The reminder is 10. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}