Evaluate
\frac{196}{65}\approx 3.015384615
Factor
\frac{2 ^ {2} \cdot 7 ^ {2}}{5 \cdot 13} = 3\frac{1}{65} = 3.0153846153846153
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)196}\\\end{array}
Use the 1^{st} digit 1 from dividend 196
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)196}\\\end{array}
Since 1 is less than 65, use the next digit 9 from dividend 196 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)196}\\\end{array}
Use the 2^{nd} digit 9 from dividend 196
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)196}\\\end{array}
Since 19 is less than 65, use the next digit 6 from dividend 196 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)196}\\\end{array}
Use the 3^{rd} digit 6 from dividend 196
\begin{array}{l}\phantom{65)}003\phantom{6}\\65\overline{)196}\\\phantom{65)}\underline{\phantom{}195\phantom{}}\\\phantom{65)99}1\\\end{array}
Find closest multiple of 65 to 196. We see that 3 \times 65 = 195 is the nearest. Now subtract 195 from 196 to get reminder 1. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }1
Since 1 is less than 65, stop the division. The reminder is 1. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}