Evaluate
\frac{38}{3}\approx 12.666666667
Factor
\frac{2 \cdot 19}{3} = 12\frac{2}{3} = 12.666666666666666
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)152}\\\end{array}
Use the 1^{st} digit 1 from dividend 152
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)152}\\\end{array}
Since 1 is less than 12, use the next digit 5 from dividend 152 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)152}\\\end{array}
Use the 2^{nd} digit 5 from dividend 152
\begin{array}{l}\phantom{12)}01\phantom{4}\\12\overline{)152}\\\phantom{12)}\underline{\phantom{}12\phantom{9}}\\\phantom{12)9}3\\\end{array}
Find closest multiple of 12 to 15. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 15 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{12)}01\phantom{5}\\12\overline{)152}\\\phantom{12)}\underline{\phantom{}12\phantom{9}}\\\phantom{12)9}32\\\end{array}
Use the 3^{rd} digit 2 from dividend 152
\begin{array}{l}\phantom{12)}012\phantom{6}\\12\overline{)152}\\\phantom{12)}\underline{\phantom{}12\phantom{9}}\\\phantom{12)9}32\\\phantom{12)}\underline{\phantom{9}24\phantom{}}\\\phantom{12)99}8\\\end{array}
Find closest multiple of 12 to 32. We see that 2 \times 12 = 24 is the nearest. Now subtract 24 from 32 to get reminder 8. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }8
Since 8 is less than 12, stop the division. The reminder is 8. 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}