Evaluate
\frac{98}{65}\approx 1.507692308
Factor
\frac{2 \cdot 7 ^ {2}}{5 \cdot 13} = 1\frac{33}{65} = 1.5076923076923077
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)98}\\\end{array}
Use the 1^{st} digit 9 from dividend 98
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)98}\\\end{array}
Since 9 is less than 65, use the next digit 8 from dividend 98 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)98}\\\end{array}
Use the 2^{nd} digit 8 from dividend 98
\begin{array}{l}\phantom{65)}01\phantom{4}\\65\overline{)98}\\\phantom{65)}\underline{\phantom{}65\phantom{}}\\\phantom{65)}33\\\end{array}
Find closest multiple of 65 to 98. We see that 1 \times 65 = 65 is the nearest. Now subtract 65 from 98 to get reminder 33. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }33
Since 33 is less than 65, stop the division. The reminder is 33. 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}