Evaluate
5
Factor
5
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\begin{array}{l}\phantom{122)}\phantom{1}\\122\overline{)610}\\\end{array}
Use the 1^{st} digit 6 from dividend 610
\begin{array}{l}\phantom{122)}0\phantom{2}\\122\overline{)610}\\\end{array}
Since 6 is less than 122, use the next digit 1 from dividend 610 and add 0 to the quotient
\begin{array}{l}\phantom{122)}0\phantom{3}\\122\overline{)610}\\\end{array}
Use the 2^{nd} digit 1 from dividend 610
\begin{array}{l}\phantom{122)}00\phantom{4}\\122\overline{)610}\\\end{array}
Since 61 is less than 122, use the next digit 0 from dividend 610 and add 0 to the quotient
\begin{array}{l}\phantom{122)}00\phantom{5}\\122\overline{)610}\\\end{array}
Use the 3^{rd} digit 0 from dividend 610
\begin{array}{l}\phantom{122)}005\phantom{6}\\122\overline{)610}\\\phantom{122)}\underline{\phantom{}610\phantom{}}\\\phantom{122)999}0\\\end{array}
Find closest multiple of 122 to 610. We see that 5 \times 122 = 610 is the nearest. Now subtract 610 from 610 to get reminder 0. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }0
Since 0 is less than 122, stop the division. The reminder is 0. 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}