Evaluate
\frac{260}{27}\approx 9.62962963
Factor
\frac{2 ^ {2} \cdot 5 \cdot 13}{3 ^ {3}} = 9\frac{17}{27} = 9.62962962962963
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)520}\\\end{array}
Use the 1^{st} digit 5 from dividend 520
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)520}\\\end{array}
Since 5 is less than 54, use the next digit 2 from dividend 520 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)520}\\\end{array}
Use the 2^{nd} digit 2 from dividend 520
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)520}\\\end{array}
Since 52 is less than 54, use the next digit 0 from dividend 520 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)520}\\\end{array}
Use the 3^{rd} digit 0 from dividend 520
\begin{array}{l}\phantom{54)}009\phantom{6}\\54\overline{)520}\\\phantom{54)}\underline{\phantom{}486\phantom{}}\\\phantom{54)9}34\\\end{array}
Find closest multiple of 54 to 520. We see that 9 \times 54 = 486 is the nearest. Now subtract 486 from 520 to get reminder 34. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }34
Since 34 is less than 54, stop the division. The reminder is 34. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}