Evaluate
\frac{21}{13}\approx 1.615384615
Factor
\frac{3 \cdot 7}{13} = 1\frac{8}{13} = 1.6153846153846154
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)21}\\\end{array}
Use the 1^{st} digit 2 from dividend 21
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)21}\\\end{array}
Since 2 is less than 13, use the next digit 1 from dividend 21 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)21}\\\end{array}
Use the 2^{nd} digit 1 from dividend 21
\begin{array}{l}\phantom{13)}01\phantom{4}\\13\overline{)21}\\\phantom{13)}\underline{\phantom{}13\phantom{}}\\\phantom{13)9}8\\\end{array}
Find closest multiple of 13 to 21. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 21 to get reminder 8. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }8
Since 8 is less than 13, stop the division. The reminder is 8. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}