Evaluate
\frac{98}{33}\approx 2.96969697
Factor
\frac{2 \cdot 7 ^ {2}}{3 \cdot 11} = 2\frac{32}{33} = 2.9696969696969697
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)98}\\\end{array}
Use the 1^{st} digit 9 from dividend 98
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)98}\\\end{array}
Since 9 is less than 33, use the next digit 8 from dividend 98 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)98}\\\end{array}
Use the 2^{nd} digit 8 from dividend 98
\begin{array}{l}\phantom{33)}02\phantom{4}\\33\overline{)98}\\\phantom{33)}\underline{\phantom{}66\phantom{}}\\\phantom{33)}32\\\end{array}
Find closest multiple of 33 to 98. We see that 2 \times 33 = 66 is the nearest. Now subtract 66 from 98 to get reminder 32. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }32
Since 32 is less than 33, stop the division. The reminder is 32. 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}