Evaluate
\frac{52}{27}\approx 1.925925926
Factor
\frac{2 ^ {2} \cdot 13}{3 ^ {3}} = 1\frac{25}{27} = 1.9259259259259258
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)52}\\\end{array}
Use the 1^{st} digit 5 from dividend 52
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)52}\\\end{array}
Since 5 is less than 27, use the next digit 2 from dividend 52 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)52}\\\end{array}
Use the 2^{nd} digit 2 from dividend 52
\begin{array}{l}\phantom{27)}01\phantom{4}\\27\overline{)52}\\\phantom{27)}\underline{\phantom{}27\phantom{}}\\\phantom{27)}25\\\end{array}
Find closest multiple of 27 to 52. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 52 to get reminder 25. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }25
Since 25 is less than 27, stop the division. The reminder is 25. The topmost line 01 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}