Evaluate
\frac{27}{2}=13.5
Factor
\frac{3 ^ {3}}{2} = 13\frac{1}{2} = 13.5
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\begin{array}{l}\phantom{24)}\phantom{1}\\24\overline{)324}\\\end{array}
Use the 1^{st} digit 3 from dividend 324
\begin{array}{l}\phantom{24)}0\phantom{2}\\24\overline{)324}\\\end{array}
Since 3 is less than 24, use the next digit 2 from dividend 324 and add 0 to the quotient
\begin{array}{l}\phantom{24)}0\phantom{3}\\24\overline{)324}\\\end{array}
Use the 2^{nd} digit 2 from dividend 324
\begin{array}{l}\phantom{24)}01\phantom{4}\\24\overline{)324}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}8\\\end{array}
Find closest multiple of 24 to 32. We see that 1 \times 24 = 24 is the nearest. Now subtract 24 from 32 to get reminder 8. Add 1 to quotient.
\begin{array}{l}\phantom{24)}01\phantom{5}\\24\overline{)324}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}84\\\end{array}
Use the 3^{rd} digit 4 from dividend 324
\begin{array}{l}\phantom{24)}013\phantom{6}\\24\overline{)324}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}84\\\phantom{24)}\underline{\phantom{9}72\phantom{}}\\\phantom{24)9}12\\\end{array}
Find closest multiple of 24 to 84. We see that 3 \times 24 = 72 is the nearest. Now subtract 72 from 84 to get reminder 12. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }12
Since 12 is less than 24, stop the division. The reminder is 12. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}