Evaluate
\frac{324}{25}=12.96
Factor
\frac{2 ^ {2} \cdot 3 ^ {4}}{5 ^ {2}} = 12\frac{24}{25} = 12.96
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)324}\\\end{array}
Use the 1^{st} digit 3 from dividend 324
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)324}\\\end{array}
Since 3 is less than 25, use the next digit 2 from dividend 324 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)324}\\\end{array}
Use the 2^{nd} digit 2 from dividend 324
\begin{array}{l}\phantom{25)}01\phantom{4}\\25\overline{)324}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}7\\\end{array}
Find closest multiple of 25 to 32. We see that 1 \times 25 = 25 is the nearest. Now subtract 25 from 32 to get reminder 7. Add 1 to quotient.
\begin{array}{l}\phantom{25)}01\phantom{5}\\25\overline{)324}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}74\\\end{array}
Use the 3^{rd} digit 4 from dividend 324
\begin{array}{l}\phantom{25)}012\phantom{6}\\25\overline{)324}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}74\\\phantom{25)}\underline{\phantom{9}50\phantom{}}\\\phantom{25)9}24\\\end{array}
Find closest multiple of 25 to 74. We see that 2 \times 25 = 50 is the nearest. Now subtract 50 from 74 to get reminder 24. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }24
Since 24 is less than 25, stop the division. The reminder is 24. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}