Evaluate
\frac{40}{13}\approx 3.076923077
Factor
\frac{2 ^ {3} \cdot 5}{13} = 3\frac{1}{13} = 3.076923076923077
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\begin{array}{l}\phantom{195)}\phantom{1}\\195\overline{)600}\\\end{array}
Use the 1^{st} digit 6 from dividend 600
\begin{array}{l}\phantom{195)}0\phantom{2}\\195\overline{)600}\\\end{array}
Since 6 is less than 195, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{195)}0\phantom{3}\\195\overline{)600}\\\end{array}
Use the 2^{nd} digit 0 from dividend 600
\begin{array}{l}\phantom{195)}00\phantom{4}\\195\overline{)600}\\\end{array}
Since 60 is less than 195, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{195)}00\phantom{5}\\195\overline{)600}\\\end{array}
Use the 3^{rd} digit 0 from dividend 600
\begin{array}{l}\phantom{195)}003\phantom{6}\\195\overline{)600}\\\phantom{195)}\underline{\phantom{}585\phantom{}}\\\phantom{195)9}15\\\end{array}
Find closest multiple of 195 to 600. We see that 3 \times 195 = 585 is the nearest. Now subtract 585 from 600 to get reminder 15. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }15
Since 15 is less than 195, stop the division. The reminder is 15. 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}