Evaluate
\frac{627}{50}=12.54
Factor
\frac{3 \cdot 11 \cdot 19}{2 \cdot 5 ^ {2}} = 12\frac{27}{50} = 12.54
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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)12540}\\\end{array}
Use the 1^{st} digit 1 from dividend 12540
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)12540}\\\end{array}
Since 1 is less than 1000, use the next digit 2 from dividend 12540 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)12540}\\\end{array}
Use the 2^{nd} digit 2 from dividend 12540
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)12540}\\\end{array}
Since 12 is less than 1000, use the next digit 5 from dividend 12540 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)12540}\\\end{array}
Use the 3^{rd} digit 5 from dividend 12540
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)12540}\\\end{array}
Since 125 is less than 1000, use the next digit 4 from dividend 12540 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)12540}\\\end{array}
Use the 4^{th} digit 4 from dividend 12540
\begin{array}{l}\phantom{1000)}0001\phantom{8}\\1000\overline{)12540}\\\phantom{1000)}\underline{\phantom{}1000\phantom{9}}\\\phantom{1000)9}254\\\end{array}
Find closest multiple of 1000 to 1254. We see that 1 \times 1000 = 1000 is the nearest. Now subtract 1000 from 1254 to get reminder 254. Add 1 to quotient.
\begin{array}{l}\phantom{1000)}0001\phantom{9}\\1000\overline{)12540}\\\phantom{1000)}\underline{\phantom{}1000\phantom{9}}\\\phantom{1000)9}2540\\\end{array}
Use the 5^{th} digit 0 from dividend 12540
\begin{array}{l}\phantom{1000)}00012\phantom{10}\\1000\overline{)12540}\\\phantom{1000)}\underline{\phantom{}1000\phantom{9}}\\\phantom{1000)9}2540\\\phantom{1000)}\underline{\phantom{9}2000\phantom{}}\\\phantom{1000)99}540\\\end{array}
Find closest multiple of 1000 to 2540. We see that 2 \times 1000 = 2000 is the nearest. Now subtract 2000 from 2540 to get reminder 540. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }540
Since 540 is less than 1000, stop the division. The reminder is 540. The topmost line 00012 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}