Evaluate
\frac{13}{2}=6.5
Factor
\frac{13}{2} = 6\frac{1}{2} = 6.5
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)650}\\\end{array}
Use the 1^{st} digit 6 from dividend 650
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)650}\\\end{array}
Since 6 is less than 100, use the next digit 5 from dividend 650 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)650}\\\end{array}
Use the 2^{nd} digit 5 from dividend 650
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)650}\\\end{array}
Since 65 is less than 100, use the next digit 0 from dividend 650 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)650}\\\end{array}
Use the 3^{rd} digit 0 from dividend 650
\begin{array}{l}\phantom{100)}006\phantom{6}\\100\overline{)650}\\\phantom{100)}\underline{\phantom{}600\phantom{}}\\\phantom{100)9}50\\\end{array}
Find closest multiple of 100 to 650. We see that 6 \times 100 = 600 is the nearest. Now subtract 600 from 650 to get reminder 50. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }50
Since 50 is less than 100, stop the division. The reminder is 50. 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}