Evaluate
\frac{13}{2}=6.5
Factor
\frac{13}{2} = 6\frac{1}{2} = 6.5
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\begin{array}{l}\phantom{64)}\phantom{1}\\64\overline{)416}\\\end{array}
Use the 1^{st} digit 4 from dividend 416
\begin{array}{l}\phantom{64)}0\phantom{2}\\64\overline{)416}\\\end{array}
Since 4 is less than 64, use the next digit 1 from dividend 416 and add 0 to the quotient
\begin{array}{l}\phantom{64)}0\phantom{3}\\64\overline{)416}\\\end{array}
Use the 2^{nd} digit 1 from dividend 416
\begin{array}{l}\phantom{64)}00\phantom{4}\\64\overline{)416}\\\end{array}
Since 41 is less than 64, use the next digit 6 from dividend 416 and add 0 to the quotient
\begin{array}{l}\phantom{64)}00\phantom{5}\\64\overline{)416}\\\end{array}
Use the 3^{rd} digit 6 from dividend 416
\begin{array}{l}\phantom{64)}006\phantom{6}\\64\overline{)416}\\\phantom{64)}\underline{\phantom{}384\phantom{}}\\\phantom{64)9}32\\\end{array}
Find closest multiple of 64 to 416. We see that 6 \times 64 = 384 is the nearest. Now subtract 384 from 416 to get reminder 32. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }32
Since 32 is less than 64, stop the division. The reminder is 32. 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}