Evaluate
\frac{21}{11}\approx 1.909090909
Factor
\frac{3 \cdot 7}{11} = 1\frac{10}{11} = 1.9090909090909092
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\begin{array}{l}\phantom{44)}\phantom{1}\\44\overline{)84}\\\end{array}
Use the 1^{st} digit 8 from dividend 84
\begin{array}{l}\phantom{44)}0\phantom{2}\\44\overline{)84}\\\end{array}
Since 8 is less than 44, use the next digit 4 from dividend 84 and add 0 to the quotient
\begin{array}{l}\phantom{44)}0\phantom{3}\\44\overline{)84}\\\end{array}
Use the 2^{nd} digit 4 from dividend 84
\begin{array}{l}\phantom{44)}01\phantom{4}\\44\overline{)84}\\\phantom{44)}\underline{\phantom{}44\phantom{}}\\\phantom{44)}40\\\end{array}
Find closest multiple of 44 to 84. We see that 1 \times 44 = 44 is the nearest. Now subtract 44 from 84 to get reminder 40. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }40
Since 40 is less than 44, stop the division. The reminder is 40. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}