Evaluate
\frac{196}{39}\approx 5.025641026
Factor
\frac{2 ^ {2} \cdot 7 ^ {2}}{3 \cdot 13} = 5\frac{1}{39} = 5.0256410256410255
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\begin{array}{l}\phantom{39)}\phantom{1}\\39\overline{)196}\\\end{array}
Use the 1^{st} digit 1 from dividend 196
\begin{array}{l}\phantom{39)}0\phantom{2}\\39\overline{)196}\\\end{array}
Since 1 is less than 39, use the next digit 9 from dividend 196 and add 0 to the quotient
\begin{array}{l}\phantom{39)}0\phantom{3}\\39\overline{)196}\\\end{array}
Use the 2^{nd} digit 9 from dividend 196
\begin{array}{l}\phantom{39)}00\phantom{4}\\39\overline{)196}\\\end{array}
Since 19 is less than 39, use the next digit 6 from dividend 196 and add 0 to the quotient
\begin{array}{l}\phantom{39)}00\phantom{5}\\39\overline{)196}\\\end{array}
Use the 3^{rd} digit 6 from dividend 196
\begin{array}{l}\phantom{39)}005\phantom{6}\\39\overline{)196}\\\phantom{39)}\underline{\phantom{}195\phantom{}}\\\phantom{39)99}1\\\end{array}
Find closest multiple of 39 to 196. We see that 5 \times 39 = 195 is the nearest. Now subtract 195 from 196 to get reminder 1. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }1
Since 1 is less than 39, stop the division. The reminder is 1. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}