Evaluate
\frac{77}{25}=3.08
Factor
\frac{7 \cdot 11}{5 ^ {2}} = 3\frac{2}{25} = 3.08
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\begin{array}{l}\phantom{50)}\phantom{1}\\50\overline{)154}\\\end{array}
Use the 1^{st} digit 1 from dividend 154
\begin{array}{l}\phantom{50)}0\phantom{2}\\50\overline{)154}\\\end{array}
Since 1 is less than 50, use the next digit 5 from dividend 154 and add 0 to the quotient
\begin{array}{l}\phantom{50)}0\phantom{3}\\50\overline{)154}\\\end{array}
Use the 2^{nd} digit 5 from dividend 154
\begin{array}{l}\phantom{50)}00\phantom{4}\\50\overline{)154}\\\end{array}
Since 15 is less than 50, use the next digit 4 from dividend 154 and add 0 to the quotient
\begin{array}{l}\phantom{50)}00\phantom{5}\\50\overline{)154}\\\end{array}
Use the 3^{rd} digit 4 from dividend 154
\begin{array}{l}\phantom{50)}003\phantom{6}\\50\overline{)154}\\\phantom{50)}\underline{\phantom{}150\phantom{}}\\\phantom{50)99}4\\\end{array}
Find closest multiple of 50 to 154. We see that 3 \times 50 = 150 is the nearest. Now subtract 150 from 154 to get reminder 4. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }4
Since 4 is less than 50, stop the division. The reminder is 4. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}