Evaluate
\frac{159}{61}\approx 2.606557377
Factor
\frac{3 \cdot 53}{61} = 2\frac{37}{61} = 2.6065573770491803
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\begin{array}{l}\phantom{122)}\phantom{1}\\122\overline{)318}\\\end{array}
Use the 1^{st} digit 3 from dividend 318
\begin{array}{l}\phantom{122)}0\phantom{2}\\122\overline{)318}\\\end{array}
Since 3 is less than 122, use the next digit 1 from dividend 318 and add 0 to the quotient
\begin{array}{l}\phantom{122)}0\phantom{3}\\122\overline{)318}\\\end{array}
Use the 2^{nd} digit 1 from dividend 318
\begin{array}{l}\phantom{122)}00\phantom{4}\\122\overline{)318}\\\end{array}
Since 31 is less than 122, use the next digit 8 from dividend 318 and add 0 to the quotient
\begin{array}{l}\phantom{122)}00\phantom{5}\\122\overline{)318}\\\end{array}
Use the 3^{rd} digit 8 from dividend 318
\begin{array}{l}\phantom{122)}002\phantom{6}\\122\overline{)318}\\\phantom{122)}\underline{\phantom{}244\phantom{}}\\\phantom{122)9}74\\\end{array}
Find closest multiple of 122 to 318. We see that 2 \times 122 = 244 is the nearest. Now subtract 244 from 318 to get reminder 74. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }74
Since 74 is less than 122, stop the division. The reminder is 74. 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}