Evaluate
\frac{225}{16}=14.0625
Factor
\frac{3 ^ {2} \cdot 5 ^ {2}}{2 ^ {4}} = 14\frac{1}{16} = 14.0625
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\begin{array}{l}\phantom{10000)}\phantom{1}\\10000\overline{)140625}\\\end{array}
Use the 1^{st} digit 1 from dividend 140625
\begin{array}{l}\phantom{10000)}0\phantom{2}\\10000\overline{)140625}\\\end{array}
Since 1 is less than 10000, use the next digit 4 from dividend 140625 and add 0 to the quotient
\begin{array}{l}\phantom{10000)}0\phantom{3}\\10000\overline{)140625}\\\end{array}
Use the 2^{nd} digit 4 from dividend 140625
\begin{array}{l}\phantom{10000)}00\phantom{4}\\10000\overline{)140625}\\\end{array}
Since 14 is less than 10000, use the next digit 0 from dividend 140625 and add 0 to the quotient
\begin{array}{l}\phantom{10000)}00\phantom{5}\\10000\overline{)140625}\\\end{array}
Use the 3^{rd} digit 0 from dividend 140625
\begin{array}{l}\phantom{10000)}000\phantom{6}\\10000\overline{)140625}\\\end{array}
Since 140 is less than 10000, use the next digit 6 from dividend 140625 and add 0 to the quotient
\begin{array}{l}\phantom{10000)}000\phantom{7}\\10000\overline{)140625}\\\end{array}
Use the 4^{th} digit 6 from dividend 140625
\begin{array}{l}\phantom{10000)}0000\phantom{8}\\10000\overline{)140625}\\\end{array}
Since 1406 is less than 10000, use the next digit 2 from dividend 140625 and add 0 to the quotient
\begin{array}{l}\phantom{10000)}0000\phantom{9}\\10000\overline{)140625}\\\end{array}
Use the 5^{th} digit 2 from dividend 140625
\begin{array}{l}\phantom{10000)}00001\phantom{10}\\10000\overline{)140625}\\\phantom{10000)}\underline{\phantom{}10000\phantom{9}}\\\phantom{10000)9}4062\\\end{array}
Find closest multiple of 10000 to 14062. We see that 1 \times 10000 = 10000 is the nearest. Now subtract 10000 from 14062 to get reminder 4062. Add 1 to quotient.
\begin{array}{l}\phantom{10000)}00001\phantom{11}\\10000\overline{)140625}\\\phantom{10000)}\underline{\phantom{}10000\phantom{9}}\\\phantom{10000)9}40625\\\end{array}
Use the 6^{th} digit 5 from dividend 140625
\begin{array}{l}\phantom{10000)}000014\phantom{12}\\10000\overline{)140625}\\\phantom{10000)}\underline{\phantom{}10000\phantom{9}}\\\phantom{10000)9}40625\\\phantom{10000)}\underline{\phantom{9}40000\phantom{}}\\\phantom{10000)999}625\\\end{array}
Find closest multiple of 10000 to 40625. We see that 4 \times 10000 = 40000 is the nearest. Now subtract 40000 from 40625 to get reminder 625. Add 4 to quotient.
\text{Quotient: }14 \text{Reminder: }625
Since 625 is less than 10000, stop the division. The reminder is 625. The topmost line 000014 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 14.
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}