Evaluate
\frac{77}{19}\approx 4.052631579
Factor
\frac{7 \cdot 11}{19} = 4\frac{1}{19} = 4.052631578947368
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\begin{array}{l}\phantom{19)}\phantom{1}\\19\overline{)77}\\\end{array}
Use the 1^{st} digit 7 from dividend 77
\begin{array}{l}\phantom{19)}0\phantom{2}\\19\overline{)77}\\\end{array}
Since 7 is less than 19, use the next digit 7 from dividend 77 and add 0 to the quotient
\begin{array}{l}\phantom{19)}0\phantom{3}\\19\overline{)77}\\\end{array}
Use the 2^{nd} digit 7 from dividend 77
\begin{array}{l}\phantom{19)}04\phantom{4}\\19\overline{)77}\\\phantom{19)}\underline{\phantom{}76\phantom{}}\\\phantom{19)9}1\\\end{array}
Find closest multiple of 19 to 77. We see that 4 \times 19 = 76 is the nearest. Now subtract 76 from 77 to get reminder 1. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }1
Since 1 is less than 19, stop the division. The reminder is 1. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}