Evaluate
\frac{86}{11}\approx 7.818181818
Factor
\frac{2 \cdot 43}{11} = 7\frac{9}{11} = 7.818181818181818
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)172}\\\end{array}
Use the 1^{st} digit 1 from dividend 172
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)172}\\\end{array}
Since 1 is less than 22, use the next digit 7 from dividend 172 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)172}\\\end{array}
Use the 2^{nd} digit 7 from dividend 172
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)172}\\\end{array}
Since 17 is less than 22, use the next digit 2 from dividend 172 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)172}\\\end{array}
Use the 3^{rd} digit 2 from dividend 172
\begin{array}{l}\phantom{22)}007\phantom{6}\\22\overline{)172}\\\phantom{22)}\underline{\phantom{}154\phantom{}}\\\phantom{22)9}18\\\end{array}
Find closest multiple of 22 to 172. We see that 7 \times 22 = 154 is the nearest. Now subtract 154 from 172 to get reminder 18. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }18
Since 18 is less than 22, stop the division. The reminder is 18. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}