Evaluate
\frac{145}{12}\approx 12.083333333
Factor
\frac{5 \cdot 29}{2 ^ {2} \cdot 3} = 12\frac{1}{12} = 12.083333333333334
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\begin{array}{l}\phantom{24)}\phantom{1}\\24\overline{)290}\\\end{array}
Use the 1^{st} digit 2 from dividend 290
\begin{array}{l}\phantom{24)}0\phantom{2}\\24\overline{)290}\\\end{array}
Since 2 is less than 24, use the next digit 9 from dividend 290 and add 0 to the quotient
\begin{array}{l}\phantom{24)}0\phantom{3}\\24\overline{)290}\\\end{array}
Use the 2^{nd} digit 9 from dividend 290
\begin{array}{l}\phantom{24)}01\phantom{4}\\24\overline{)290}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}5\\\end{array}
Find closest multiple of 24 to 29. We see that 1 \times 24 = 24 is the nearest. Now subtract 24 from 29 to get reminder 5. Add 1 to quotient.
\begin{array}{l}\phantom{24)}01\phantom{5}\\24\overline{)290}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}50\\\end{array}
Use the 3^{rd} digit 0 from dividend 290
\begin{array}{l}\phantom{24)}012\phantom{6}\\24\overline{)290}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}50\\\phantom{24)}\underline{\phantom{9}48\phantom{}}\\\phantom{24)99}2\\\end{array}
Find closest multiple of 24 to 50. We see that 2 \times 24 = 48 is the nearest. Now subtract 48 from 50 to get reminder 2. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }2
Since 2 is less than 24, stop the division. The reminder is 2. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}