Evaluate
\frac{52}{9}\approx 5.777777778
Factor
\frac{2 ^ {2} \cdot 13}{3 ^ {2}} = 5\frac{7}{9} = 5.777777777777778
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)104}\\\end{array}
Use the 1^{st} digit 1 from dividend 104
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)104}\\\end{array}
Since 1 is less than 18, use the next digit 0 from dividend 104 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)104}\\\end{array}
Use the 2^{nd} digit 0 from dividend 104
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)104}\\\end{array}
Since 10 is less than 18, use the next digit 4 from dividend 104 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)104}\\\end{array}
Use the 3^{rd} digit 4 from dividend 104
\begin{array}{l}\phantom{18)}005\phantom{6}\\18\overline{)104}\\\phantom{18)}\underline{\phantom{9}90\phantom{}}\\\phantom{18)9}14\\\end{array}
Find closest multiple of 18 to 104. We see that 5 \times 18 = 90 is the nearest. Now subtract 90 from 104 to get reminder 14. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }14
Since 14 is less than 18, stop the division. The reminder is 14. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}