Evaluate
\frac{77}{29}\approx 2.655172414
Factor
\frac{7 \cdot 11}{29} = 2\frac{19}{29} = 2.6551724137931036
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\begin{array}{l}\phantom{58)}\phantom{1}\\58\overline{)154}\\\end{array}
Use the 1^{st} digit 1 from dividend 154
\begin{array}{l}\phantom{58)}0\phantom{2}\\58\overline{)154}\\\end{array}
Since 1 is less than 58, use the next digit 5 from dividend 154 and add 0 to the quotient
\begin{array}{l}\phantom{58)}0\phantom{3}\\58\overline{)154}\\\end{array}
Use the 2^{nd} digit 5 from dividend 154
\begin{array}{l}\phantom{58)}00\phantom{4}\\58\overline{)154}\\\end{array}
Since 15 is less than 58, use the next digit 4 from dividend 154 and add 0 to the quotient
\begin{array}{l}\phantom{58)}00\phantom{5}\\58\overline{)154}\\\end{array}
Use the 3^{rd} digit 4 from dividend 154
\begin{array}{l}\phantom{58)}002\phantom{6}\\58\overline{)154}\\\phantom{58)}\underline{\phantom{}116\phantom{}}\\\phantom{58)9}38\\\end{array}
Find closest multiple of 58 to 154. We see that 2 \times 58 = 116 is the nearest. Now subtract 116 from 154 to get reminder 38. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }38
Since 38 is less than 58, stop the division. The reminder is 38. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}