Evaluate
\frac{108}{77}\approx 1.402597403
Factor
\frac{2 ^ {2} \cdot 3 ^ {3}}{7 \cdot 11} = 1\frac{31}{77} = 1.4025974025974026
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\begin{array}{l}\phantom{2310)}\phantom{1}\\2310\overline{)3240}\\\end{array}
Use the 1^{st} digit 3 from dividend 3240
\begin{array}{l}\phantom{2310)}0\phantom{2}\\2310\overline{)3240}\\\end{array}
Since 3 is less than 2310, use the next digit 2 from dividend 3240 and add 0 to the quotient
\begin{array}{l}\phantom{2310)}0\phantom{3}\\2310\overline{)3240}\\\end{array}
Use the 2^{nd} digit 2 from dividend 3240
\begin{array}{l}\phantom{2310)}00\phantom{4}\\2310\overline{)3240}\\\end{array}
Since 32 is less than 2310, use the next digit 4 from dividend 3240 and add 0 to the quotient
\begin{array}{l}\phantom{2310)}00\phantom{5}\\2310\overline{)3240}\\\end{array}
Use the 3^{rd} digit 4 from dividend 3240
\begin{array}{l}\phantom{2310)}000\phantom{6}\\2310\overline{)3240}\\\end{array}
Since 324 is less than 2310, use the next digit 0 from dividend 3240 and add 0 to the quotient
\begin{array}{l}\phantom{2310)}000\phantom{7}\\2310\overline{)3240}\\\end{array}
Use the 4^{th} digit 0 from dividend 3240
\begin{array}{l}\phantom{2310)}0001\phantom{8}\\2310\overline{)3240}\\\phantom{2310)}\underline{\phantom{}2310\phantom{}}\\\phantom{2310)9}930\\\end{array}
Find closest multiple of 2310 to 3240. We see that 1 \times 2310 = 2310 is the nearest. Now subtract 2310 from 3240 to get reminder 930. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }930
Since 930 is less than 2310, stop the division. The reminder is 930. The topmost line 0001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}