Evaluate
\frac{625}{3}\approx 208.333333333
Factor
\frac{5 ^ {4}}{3} = 208\frac{1}{3} = 208.33333333333334
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)2500}\\\end{array}
Use the 1^{st} digit 2 from dividend 2500
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)2500}\\\end{array}
Since 2 is less than 12, use the next digit 5 from dividend 2500 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)2500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 2500
\begin{array}{l}\phantom{12)}02\phantom{4}\\12\overline{)2500}\\\phantom{12)}\underline{\phantom{}24\phantom{99}}\\\phantom{12)9}1\\\end{array}
Find closest multiple of 12 to 25. We see that 2 \times 12 = 24 is the nearest. Now subtract 24 from 25 to get reminder 1. Add 2 to quotient.
\begin{array}{l}\phantom{12)}02\phantom{5}\\12\overline{)2500}\\\phantom{12)}\underline{\phantom{}24\phantom{99}}\\\phantom{12)9}10\\\end{array}
Use the 3^{rd} digit 0 from dividend 2500
\begin{array}{l}\phantom{12)}020\phantom{6}\\12\overline{)2500}\\\phantom{12)}\underline{\phantom{}24\phantom{99}}\\\phantom{12)9}10\\\end{array}
Since 10 is less than 12, use the next digit 0 from dividend 2500 and add 0 to the quotient
\begin{array}{l}\phantom{12)}020\phantom{7}\\12\overline{)2500}\\\phantom{12)}\underline{\phantom{}24\phantom{99}}\\\phantom{12)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 2500
\begin{array}{l}\phantom{12)}0208\phantom{8}\\12\overline{)2500}\\\phantom{12)}\underline{\phantom{}24\phantom{99}}\\\phantom{12)9}100\\\phantom{12)}\underline{\phantom{99}96\phantom{}}\\\phantom{12)999}4\\\end{array}
Find closest multiple of 12 to 100. We see that 8 \times 12 = 96 is the nearest. Now subtract 96 from 100 to get reminder 4. Add 8 to quotient.
\text{Quotient: }208 \text{Reminder: }4
Since 4 is less than 12, stop the division. The reminder is 4. The topmost line 0208 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 208.
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}