Evaluate
\frac{59}{11}\approx 5.363636364
Factor
\frac{59}{11} = 5\frac{4}{11} = 5.363636363636363
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)118}\\\end{array}
Use the 1^{st} digit 1 from dividend 118
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)118}\\\end{array}
Since 1 is less than 22, use the next digit 1 from dividend 118 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)118}\\\end{array}
Use the 2^{nd} digit 1 from dividend 118
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)118}\\\end{array}
Since 11 is less than 22, use the next digit 8 from dividend 118 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)118}\\\end{array}
Use the 3^{rd} digit 8 from dividend 118
\begin{array}{l}\phantom{22)}005\phantom{6}\\22\overline{)118}\\\phantom{22)}\underline{\phantom{}110\phantom{}}\\\phantom{22)99}8\\\end{array}
Find closest multiple of 22 to 118. We see that 5 \times 22 = 110 is the nearest. Now subtract 110 from 118 to get reminder 8. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }8
Since 8 is less than 22, stop the division. The reminder is 8. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}