Evaluate
\frac{67}{11}\approx 6.090909091
Factor
\frac{67}{11} = 6\frac{1}{11} = 6.090909090909091
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)134}\\\end{array}
Use the 1^{st} digit 1 from dividend 134
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)134}\\\end{array}
Since 1 is less than 22, use the next digit 3 from dividend 134 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)134}\\\end{array}
Use the 2^{nd} digit 3 from dividend 134
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)134}\\\end{array}
Since 13 is less than 22, use the next digit 4 from dividend 134 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)134}\\\end{array}
Use the 3^{rd} digit 4 from dividend 134
\begin{array}{l}\phantom{22)}006\phantom{6}\\22\overline{)134}\\\phantom{22)}\underline{\phantom{}132\phantom{}}\\\phantom{22)99}2\\\end{array}
Find closest multiple of 22 to 134. We see that 6 \times 22 = 132 is the nearest. Now subtract 132 from 134 to get reminder 2. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }2
Since 2 is less than 22, stop the division. The reminder is 2. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}