Evaluate
\frac{113}{4}=28.25
Factor
\frac{113}{2 ^ {2}} = 28\frac{1}{4} = 28.25
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)339}\\\end{array}
Use the 1^{st} digit 3 from dividend 339
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)339}\\\end{array}
Since 3 is less than 12, use the next digit 3 from dividend 339 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)339}\\\end{array}
Use the 2^{nd} digit 3 from dividend 339
\begin{array}{l}\phantom{12)}02\phantom{4}\\12\overline{)339}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}9\\\end{array}
Find closest multiple of 12 to 33. We see that 2 \times 12 = 24 is the nearest. Now subtract 24 from 33 to get reminder 9. Add 2 to quotient.
\begin{array}{l}\phantom{12)}02\phantom{5}\\12\overline{)339}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}99\\\end{array}
Use the 3^{rd} digit 9 from dividend 339
\begin{array}{l}\phantom{12)}028\phantom{6}\\12\overline{)339}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}99\\\phantom{12)}\underline{\phantom{9}96\phantom{}}\\\phantom{12)99}3\\\end{array}
Find closest multiple of 12 to 99. We see that 8 \times 12 = 96 is the nearest. Now subtract 96 from 99 to get reminder 3. Add 8 to quotient.
\text{Quotient: }28 \text{Reminder: }3
Since 3 is less than 12, stop the division. The reminder is 3. The topmost line 028 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 28.
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}