Evaluate
\frac{25}{3}\approx 8.333333333
Factor
\frac{5 ^ {2}}{3} = 8\frac{1}{3} = 8.333333333333334
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)225}\\\end{array}
Use the 1^{st} digit 2 from dividend 225
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)225}\\\end{array}
Since 2 is less than 27, use the next digit 2 from dividend 225 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)225}\\\end{array}
Use the 2^{nd} digit 2 from dividend 225
\begin{array}{l}\phantom{27)}00\phantom{4}\\27\overline{)225}\\\end{array}
Since 22 is less than 27, use the next digit 5 from dividend 225 and add 0 to the quotient
\begin{array}{l}\phantom{27)}00\phantom{5}\\27\overline{)225}\\\end{array}
Use the 3^{rd} digit 5 from dividend 225
\begin{array}{l}\phantom{27)}008\phantom{6}\\27\overline{)225}\\\phantom{27)}\underline{\phantom{}216\phantom{}}\\\phantom{27)99}9\\\end{array}
Find closest multiple of 27 to 225. We see that 8 \times 27 = 216 is the nearest. Now subtract 216 from 225 to get reminder 9. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }9
Since 9 is less than 27, stop the division. The reminder is 9. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}