Evaluate
\frac{323}{13}\approx 24.846153846
Factor
\frac{17 \cdot 19}{13} = 24\frac{11}{13} = 24.846153846153847
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)323}\\\end{array}
Use the 1^{st} digit 3 from dividend 323
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)323}\\\end{array}
Since 3 is less than 13, use the next digit 2 from dividend 323 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)323}\\\end{array}
Use the 2^{nd} digit 2 from dividend 323
\begin{array}{l}\phantom{13)}02\phantom{4}\\13\overline{)323}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}6\\\end{array}
Find closest multiple of 13 to 32. We see that 2 \times 13 = 26 is the nearest. Now subtract 26 from 32 to get reminder 6. Add 2 to quotient.
\begin{array}{l}\phantom{13)}02\phantom{5}\\13\overline{)323}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}63\\\end{array}
Use the 3^{rd} digit 3 from dividend 323
\begin{array}{l}\phantom{13)}024\phantom{6}\\13\overline{)323}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}63\\\phantom{13)}\underline{\phantom{9}52\phantom{}}\\\phantom{13)9}11\\\end{array}
Find closest multiple of 13 to 63. We see that 4 \times 13 = 52 is the nearest. Now subtract 52 from 63 to get reminder 11. Add 4 to quotient.
\text{Quotient: }24 \text{Reminder: }11
Since 11 is less than 13, stop the division. The reminder is 11. The topmost line 024 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 24.
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}