Evaluate
\frac{280}{13}\approx 21.538461538
Factor
\frac{2 ^ {3} \cdot 5 \cdot 7}{13} = 21\frac{7}{13} = 21.53846153846154
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)280}\\\end{array}
Use the 1^{st} digit 2 from dividend 280
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)280}\\\end{array}
Since 2 is less than 13, use the next digit 8 from dividend 280 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)280}\\\end{array}
Use the 2^{nd} digit 8 from dividend 280
\begin{array}{l}\phantom{13)}02\phantom{4}\\13\overline{)280}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}2\\\end{array}
Find closest multiple of 13 to 28. We see that 2 \times 13 = 26 is the nearest. Now subtract 26 from 28 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{13)}02\phantom{5}\\13\overline{)280}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}20\\\end{array}
Use the 3^{rd} digit 0 from dividend 280
\begin{array}{l}\phantom{13)}021\phantom{6}\\13\overline{)280}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}20\\\phantom{13)}\underline{\phantom{9}13\phantom{}}\\\phantom{13)99}7\\\end{array}
Find closest multiple of 13 to 20. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 20 to get reminder 7. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }7
Since 7 is less than 13, stop the division. The reminder is 7. The topmost line 021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}