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{60)}\phantom{1}\\60\overline{)800}\\\end{array}
Use the 1^{st} digit 8 from dividend 800
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)800}\\\end{array}
Since 8 is less than 60, use the next digit 0 from dividend 800 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)800}\\\end{array}
Use the 2^{nd} digit 0 from dividend 800
\begin{array}{l}\phantom{60)}01\phantom{4}\\60\overline{)800}\\\phantom{60)}\underline{\phantom{}60\phantom{9}}\\\phantom{60)}20\\\end{array}
Find closest multiple of 60 to 80. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 80 to get reminder 20. Add 1 to quotient.
\begin{array}{l}\phantom{60)}01\phantom{5}\\60\overline{)800}\\\phantom{60)}\underline{\phantom{}60\phantom{9}}\\\phantom{60)}200\\\end{array}
Use the 3^{rd} digit 0 from dividend 800
\begin{array}{l}\phantom{60)}013\phantom{6}\\60\overline{)800}\\\phantom{60)}\underline{\phantom{}60\phantom{9}}\\\phantom{60)}200\\\phantom{60)}\underline{\phantom{}180\phantom{}}\\\phantom{60)9}20\\\end{array}
Find closest multiple of 60 to 200. We see that 3 \times 60 = 180 is the nearest. Now subtract 180 from 200 to get reminder 20. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }20
Since 20 is less than 60, stop the division. The reminder is 20. 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}