Evaluate
\frac{142}{11}\approx 12.909090909
Factor
\frac{2 \cdot 71}{11} = 12\frac{10}{11} = 12.909090909090908
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)284}\\\end{array}
Use the 1^{st} digit 2 from dividend 284
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)284}\\\end{array}
Since 2 is less than 22, use the next digit 8 from dividend 284 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)284}\\\end{array}
Use the 2^{nd} digit 8 from dividend 284
\begin{array}{l}\phantom{22)}01\phantom{4}\\22\overline{)284}\\\phantom{22)}\underline{\phantom{}22\phantom{9}}\\\phantom{22)9}6\\\end{array}
Find closest multiple of 22 to 28. We see that 1 \times 22 = 22 is the nearest. Now subtract 22 from 28 to get reminder 6. Add 1 to quotient.
\begin{array}{l}\phantom{22)}01\phantom{5}\\22\overline{)284}\\\phantom{22)}\underline{\phantom{}22\phantom{9}}\\\phantom{22)9}64\\\end{array}
Use the 3^{rd} digit 4 from dividend 284
\begin{array}{l}\phantom{22)}012\phantom{6}\\22\overline{)284}\\\phantom{22)}\underline{\phantom{}22\phantom{9}}\\\phantom{22)9}64\\\phantom{22)}\underline{\phantom{9}44\phantom{}}\\\phantom{22)9}20\\\end{array}
Find closest multiple of 22 to 64. We see that 2 \times 22 = 44 is the nearest. Now subtract 44 from 64 to get reminder 20. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }20
Since 20 is less than 22, stop the division. The reminder is 20. 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}