Evaluate
\frac{7}{3}\approx 2.333333333
Factor
\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335
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\begin{array}{l}\phantom{108)}\phantom{1}\\108\overline{)252}\\\end{array}
Use the 1^{st} digit 2 from dividend 252
\begin{array}{l}\phantom{108)}0\phantom{2}\\108\overline{)252}\\\end{array}
Since 2 is less than 108, use the next digit 5 from dividend 252 and add 0 to the quotient
\begin{array}{l}\phantom{108)}0\phantom{3}\\108\overline{)252}\\\end{array}
Use the 2^{nd} digit 5 from dividend 252
\begin{array}{l}\phantom{108)}00\phantom{4}\\108\overline{)252}\\\end{array}
Since 25 is less than 108, use the next digit 2 from dividend 252 and add 0 to the quotient
\begin{array}{l}\phantom{108)}00\phantom{5}\\108\overline{)252}\\\end{array}
Use the 3^{rd} digit 2 from dividend 252
\begin{array}{l}\phantom{108)}002\phantom{6}\\108\overline{)252}\\\phantom{108)}\underline{\phantom{}216\phantom{}}\\\phantom{108)9}36\\\end{array}
Find closest multiple of 108 to 252. We see that 2 \times 108 = 216 is the nearest. Now subtract 216 from 252 to get reminder 36. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }36
Since 36 is less than 108, stop the division. The reminder is 36. 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}