Evaluate
\frac{44}{21}\approx 2.095238095
Factor
\frac{2 ^ {2} \cdot 11}{3 \cdot 7} = 2\frac{2}{21} = 2.0952380952380953
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)88}\\\end{array}
Use the 1^{st} digit 8 from dividend 88
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)88}\\\end{array}
Since 8 is less than 42, use the next digit 8 from dividend 88 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)88}\\\end{array}
Use the 2^{nd} digit 8 from dividend 88
\begin{array}{l}\phantom{42)}02\phantom{4}\\42\overline{)88}\\\phantom{42)}\underline{\phantom{}84\phantom{}}\\\phantom{42)9}4\\\end{array}
Find closest multiple of 42 to 88. We see that 2 \times 42 = 84 is the nearest. Now subtract 84 from 88 to get reminder 4. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }4
Since 4 is less than 42, stop the division. The reminder is 4. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}