Evaluate
6
Factor
2\times 3
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\begin{array}{l}\phantom{77)}\phantom{1}\\77\overline{)462}\\\end{array}
Use the 1^{st} digit 4 from dividend 462
\begin{array}{l}\phantom{77)}0\phantom{2}\\77\overline{)462}\\\end{array}
Since 4 is less than 77, use the next digit 6 from dividend 462 and add 0 to the quotient
\begin{array}{l}\phantom{77)}0\phantom{3}\\77\overline{)462}\\\end{array}
Use the 2^{nd} digit 6 from dividend 462
\begin{array}{l}\phantom{77)}00\phantom{4}\\77\overline{)462}\\\end{array}
Since 46 is less than 77, use the next digit 2 from dividend 462 and add 0 to the quotient
\begin{array}{l}\phantom{77)}00\phantom{5}\\77\overline{)462}\\\end{array}
Use the 3^{rd} digit 2 from dividend 462
\begin{array}{l}\phantom{77)}006\phantom{6}\\77\overline{)462}\\\phantom{77)}\underline{\phantom{}462\phantom{}}\\\phantom{77)999}0\\\end{array}
Find closest multiple of 77 to 462. We see that 6 \times 77 = 462 is the nearest. Now subtract 462 from 462 to get reminder 0. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }0
Since 0 is less than 77, stop the division. The reminder is 0. 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}