Evaluate
\frac{13}{9}\approx 1.444444444
Factor
\frac{13}{3 ^ {2}} = 1\frac{4}{9} = 1.4444444444444444
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)260}\\\end{array}
Use the 1^{st} digit 2 from dividend 260
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)260}\\\end{array}
Since 2 is less than 180, use the next digit 6 from dividend 260 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)260}\\\end{array}
Use the 2^{nd} digit 6 from dividend 260
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)260}\\\end{array}
Since 26 is less than 180, use the next digit 0 from dividend 260 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)260}\\\end{array}
Use the 3^{rd} digit 0 from dividend 260
\begin{array}{l}\phantom{180)}001\phantom{6}\\180\overline{)260}\\\phantom{180)}\underline{\phantom{}180\phantom{}}\\\phantom{180)9}80\\\end{array}
Find closest multiple of 180 to 260. We see that 1 \times 180 = 180 is the nearest. Now subtract 180 from 260 to get reminder 80. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }80
Since 80 is less than 180, stop the division. The reminder is 80. The topmost line 001 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}