Evaluate
\frac{49}{34}\approx 1.441176471
Factor
\frac{7 ^ {2}}{2 \cdot 17} = 1\frac{15}{34} = 1.4411764705882353
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\begin{array}{l}\phantom{68)}\phantom{1}\\68\overline{)98}\\\end{array}
Use the 1^{st} digit 9 from dividend 98
\begin{array}{l}\phantom{68)}0\phantom{2}\\68\overline{)98}\\\end{array}
Since 9 is less than 68, use the next digit 8 from dividend 98 and add 0 to the quotient
\begin{array}{l}\phantom{68)}0\phantom{3}\\68\overline{)98}\\\end{array}
Use the 2^{nd} digit 8 from dividend 98
\begin{array}{l}\phantom{68)}01\phantom{4}\\68\overline{)98}\\\phantom{68)}\underline{\phantom{}68\phantom{}}\\\phantom{68)}30\\\end{array}
Find closest multiple of 68 to 98. We see that 1 \times 68 = 68 is the nearest. Now subtract 68 from 98 to get reminder 30. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }30
Since 30 is less than 68, stop the division. The reminder is 30. 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}