Evaluate
\frac{411}{77}\approx 5.337662338
Factor
\frac{3 \cdot 137}{7 \cdot 11} = 5\frac{26}{77} = 5.337662337662338
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\begin{array}{l}\phantom{77)}\phantom{1}\\77\overline{)411}\\\end{array}
Use the 1^{st} digit 4 from dividend 411
\begin{array}{l}\phantom{77)}0\phantom{2}\\77\overline{)411}\\\end{array}
Since 4 is less than 77, use the next digit 1 from dividend 411 and add 0 to the quotient
\begin{array}{l}\phantom{77)}0\phantom{3}\\77\overline{)411}\\\end{array}
Use the 2^{nd} digit 1 from dividend 411
\begin{array}{l}\phantom{77)}00\phantom{4}\\77\overline{)411}\\\end{array}
Since 41 is less than 77, use the next digit 1 from dividend 411 and add 0 to the quotient
\begin{array}{l}\phantom{77)}00\phantom{5}\\77\overline{)411}\\\end{array}
Use the 3^{rd} digit 1 from dividend 411
\begin{array}{l}\phantom{77)}005\phantom{6}\\77\overline{)411}\\\phantom{77)}\underline{\phantom{}385\phantom{}}\\\phantom{77)9}26\\\end{array}
Find closest multiple of 77 to 411. We see that 5 \times 77 = 385 is the nearest. Now subtract 385 from 411 to get reminder 26. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }26
Since 26 is less than 77, stop the division. The reminder is 26. 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}