Evaluate
\frac{25}{9}\approx 2.777777778
Factor
\frac{5 ^ {2}}{3 ^ {2}} = 2\frac{7}{9} = 2.7777777777777777
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\begin{array}{l}\phantom{171)}\phantom{1}\\171\overline{)475}\\\end{array}
Use the 1^{st} digit 4 from dividend 475
\begin{array}{l}\phantom{171)}0\phantom{2}\\171\overline{)475}\\\end{array}
Since 4 is less than 171, use the next digit 7 from dividend 475 and add 0 to the quotient
\begin{array}{l}\phantom{171)}0\phantom{3}\\171\overline{)475}\\\end{array}
Use the 2^{nd} digit 7 from dividend 475
\begin{array}{l}\phantom{171)}00\phantom{4}\\171\overline{)475}\\\end{array}
Since 47 is less than 171, use the next digit 5 from dividend 475 and add 0 to the quotient
\begin{array}{l}\phantom{171)}00\phantom{5}\\171\overline{)475}\\\end{array}
Use the 3^{rd} digit 5 from dividend 475
\begin{array}{l}\phantom{171)}002\phantom{6}\\171\overline{)475}\\\phantom{171)}\underline{\phantom{}342\phantom{}}\\\phantom{171)}133\\\end{array}
Find closest multiple of 171 to 475. We see that 2 \times 171 = 342 is the nearest. Now subtract 342 from 475 to get reminder 133. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }133
Since 133 is less than 171, stop the division. The reminder is 133. 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}