Evaluate
\frac{262}{41}\approx 6.390243902
Factor
\frac{2 \cdot 131}{41} = 6\frac{16}{41} = 6.390243902439025
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\begin{array}{l}\phantom{123)}\phantom{1}\\123\overline{)786}\\\end{array}
Use the 1^{st} digit 7 from dividend 786
\begin{array}{l}\phantom{123)}0\phantom{2}\\123\overline{)786}\\\end{array}
Since 7 is less than 123, use the next digit 8 from dividend 786 and add 0 to the quotient
\begin{array}{l}\phantom{123)}0\phantom{3}\\123\overline{)786}\\\end{array}
Use the 2^{nd} digit 8 from dividend 786
\begin{array}{l}\phantom{123)}00\phantom{4}\\123\overline{)786}\\\end{array}
Since 78 is less than 123, use the next digit 6 from dividend 786 and add 0 to the quotient
\begin{array}{l}\phantom{123)}00\phantom{5}\\123\overline{)786}\\\end{array}
Use the 3^{rd} digit 6 from dividend 786
\begin{array}{l}\phantom{123)}006\phantom{6}\\123\overline{)786}\\\phantom{123)}\underline{\phantom{}738\phantom{}}\\\phantom{123)9}48\\\end{array}
Find closest multiple of 123 to 786. We see that 6 \times 123 = 738 is the nearest. Now subtract 738 from 786 to get reminder 48. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }48
Since 48 is less than 123, stop the division. The reminder is 48. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}