Evaluate
\frac{13}{4}=3.25
Factor
\frac{13}{2 ^ {2}} = 3\frac{1}{4} = 3.25
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\begin{array}{l}\phantom{16)}\phantom{1}\\16\overline{)52}\\\end{array}
Use the 1^{st} digit 5 from dividend 52
\begin{array}{l}\phantom{16)}0\phantom{2}\\16\overline{)52}\\\end{array}
Since 5 is less than 16, use the next digit 2 from dividend 52 and add 0 to the quotient
\begin{array}{l}\phantom{16)}0\phantom{3}\\16\overline{)52}\\\end{array}
Use the 2^{nd} digit 2 from dividend 52
\begin{array}{l}\phantom{16)}03\phantom{4}\\16\overline{)52}\\\phantom{16)}\underline{\phantom{}48\phantom{}}\\\phantom{16)9}4\\\end{array}
Find closest multiple of 16 to 52. We see that 3 \times 16 = 48 is the nearest. Now subtract 48 from 52 to get reminder 4. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }4
Since 4 is less than 16, stop the division. The reminder is 4. The topmost line 03 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}