Evaluate
\frac{318}{25}=12.72
Factor
\frac{2 \cdot 3 \cdot 53}{5 ^ {2}} = 12\frac{18}{25} = 12.72
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)318}\\\end{array}
Use the 1^{st} digit 3 from dividend 318
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)318}\\\end{array}
Since 3 is less than 25, use the next digit 1 from dividend 318 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)318}\\\end{array}
Use the 2^{nd} digit 1 from dividend 318
\begin{array}{l}\phantom{25)}01\phantom{4}\\25\overline{)318}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}6\\\end{array}
Find closest multiple of 25 to 31. We see that 1 \times 25 = 25 is the nearest. Now subtract 25 from 31 to get reminder 6. Add 1 to quotient.
\begin{array}{l}\phantom{25)}01\phantom{5}\\25\overline{)318}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}68\\\end{array}
Use the 3^{rd} digit 8 from dividend 318
\begin{array}{l}\phantom{25)}012\phantom{6}\\25\overline{)318}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}68\\\phantom{25)}\underline{\phantom{9}50\phantom{}}\\\phantom{25)9}18\\\end{array}
Find closest multiple of 25 to 68. We see that 2 \times 25 = 50 is the nearest. Now subtract 50 from 68 to get reminder 18. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }18
Since 18 is less than 25, stop the division. The reminder is 18. 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}