Evaluate
\frac{42}{11}\approx 3.818181818
Factor
\frac{2 \cdot 3 \cdot 7}{11} = 3\frac{9}{11} = 3.8181818181818183
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\begin{array}{l}\phantom{44)}\phantom{1}\\44\overline{)168}\\\end{array}
Use the 1^{st} digit 1 from dividend 168
\begin{array}{l}\phantom{44)}0\phantom{2}\\44\overline{)168}\\\end{array}
Since 1 is less than 44, use the next digit 6 from dividend 168 and add 0 to the quotient
\begin{array}{l}\phantom{44)}0\phantom{3}\\44\overline{)168}\\\end{array}
Use the 2^{nd} digit 6 from dividend 168
\begin{array}{l}\phantom{44)}00\phantom{4}\\44\overline{)168}\\\end{array}
Since 16 is less than 44, use the next digit 8 from dividend 168 and add 0 to the quotient
\begin{array}{l}\phantom{44)}00\phantom{5}\\44\overline{)168}\\\end{array}
Use the 3^{rd} digit 8 from dividend 168
\begin{array}{l}\phantom{44)}003\phantom{6}\\44\overline{)168}\\\phantom{44)}\underline{\phantom{}132\phantom{}}\\\phantom{44)9}36\\\end{array}
Find closest multiple of 44 to 168. We see that 3 \times 44 = 132 is the nearest. Now subtract 132 from 168 to get reminder 36. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }36
Since 36 is less than 44, stop the division. The reminder is 36. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}