Evaluate
\frac{13}{5}=2.6
Factor
\frac{13}{5} = 2\frac{3}{5} = 2.6
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)91}\\\end{array}
Use the 1^{st} digit 9 from dividend 91
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)91}\\\end{array}
Since 9 is less than 35, use the next digit 1 from dividend 91 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)91}\\\end{array}
Use the 2^{nd} digit 1 from dividend 91
\begin{array}{l}\phantom{35)}02\phantom{4}\\35\overline{)91}\\\phantom{35)}\underline{\phantom{}70\phantom{}}\\\phantom{35)}21\\\end{array}
Find closest multiple of 35 to 91. We see that 2 \times 35 = 70 is the nearest. Now subtract 70 from 91 to get reminder 21. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }21
Since 21 is less than 35, stop the division. The reminder is 21. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}