Evaluate
\frac{13}{2}=6.5
Factor
\frac{13}{2} = 6\frac{1}{2} = 6.5
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\begin{array}{l}\phantom{110)}\phantom{1}\\110\overline{)715}\\\end{array}
Use the 1^{st} digit 7 from dividend 715
\begin{array}{l}\phantom{110)}0\phantom{2}\\110\overline{)715}\\\end{array}
Since 7 is less than 110, use the next digit 1 from dividend 715 and add 0 to the quotient
\begin{array}{l}\phantom{110)}0\phantom{3}\\110\overline{)715}\\\end{array}
Use the 2^{nd} digit 1 from dividend 715
\begin{array}{l}\phantom{110)}00\phantom{4}\\110\overline{)715}\\\end{array}
Since 71 is less than 110, use the next digit 5 from dividend 715 and add 0 to the quotient
\begin{array}{l}\phantom{110)}00\phantom{5}\\110\overline{)715}\\\end{array}
Use the 3^{rd} digit 5 from dividend 715
\begin{array}{l}\phantom{110)}006\phantom{6}\\110\overline{)715}\\\phantom{110)}\underline{\phantom{}660\phantom{}}\\\phantom{110)9}55\\\end{array}
Find closest multiple of 110 to 715. We see that 6 \times 110 = 660 is the nearest. Now subtract 660 from 715 to get reminder 55. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }55
Since 55 is less than 110, stop the division. The reminder is 55. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}