Evaluate
\frac{13}{3}\approx 4.333333333
Factor
\frac{13}{3} = 4\frac{1}{3} = 4.333333333333333
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)91}\\\end{array}
Use the 1^{st} digit 9 from dividend 91
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)91}\\\end{array}
Since 9 is less than 21, use the next digit 1 from dividend 91 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)91}\\\end{array}
Use the 2^{nd} digit 1 from dividend 91
\begin{array}{l}\phantom{21)}04\phantom{4}\\21\overline{)91}\\\phantom{21)}\underline{\phantom{}84\phantom{}}\\\phantom{21)9}7\\\end{array}
Find closest multiple of 21 to 91. We see that 4 \times 21 = 84 is the nearest. Now subtract 84 from 91 to get reminder 7. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }7
Since 7 is less than 21, stop the division. The reminder is 7. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}