Evaluate
\frac{8129}{125}=65.032
Factor
\frac{11 \cdot 739}{5 ^ {3}} = 65\frac{4}{125} = 65.032
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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)65032}\\\end{array}
Use the 1^{st} digit 6 from dividend 65032
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)65032}\\\end{array}
Since 6 is less than 1000, use the next digit 5 from dividend 65032 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)65032}\\\end{array}
Use the 2^{nd} digit 5 from dividend 65032
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)65032}\\\end{array}
Since 65 is less than 1000, use the next digit 0 from dividend 65032 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)65032}\\\end{array}
Use the 3^{rd} digit 0 from dividend 65032
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)65032}\\\end{array}
Since 650 is less than 1000, use the next digit 3 from dividend 65032 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)65032}\\\end{array}
Use the 4^{th} digit 3 from dividend 65032
\begin{array}{l}\phantom{1000)}0006\phantom{8}\\1000\overline{)65032}\\\phantom{1000)}\underline{\phantom{}6000\phantom{9}}\\\phantom{1000)9}503\\\end{array}
Find closest multiple of 1000 to 6503. We see that 6 \times 1000 = 6000 is the nearest. Now subtract 6000 from 6503 to get reminder 503. Add 6 to quotient.
\begin{array}{l}\phantom{1000)}0006\phantom{9}\\1000\overline{)65032}\\\phantom{1000)}\underline{\phantom{}6000\phantom{9}}\\\phantom{1000)9}5032\\\end{array}
Use the 5^{th} digit 2 from dividend 65032
\begin{array}{l}\phantom{1000)}00065\phantom{10}\\1000\overline{)65032}\\\phantom{1000)}\underline{\phantom{}6000\phantom{9}}\\\phantom{1000)9}5032\\\phantom{1000)}\underline{\phantom{9}5000\phantom{}}\\\phantom{1000)999}32\\\end{array}
Find closest multiple of 1000 to 5032. We see that 5 \times 1000 = 5000 is the nearest. Now subtract 5000 from 5032 to get reminder 32. Add 5 to quotient.
\text{Quotient: }65 \text{Reminder: }32
Since 32 is less than 1000, stop the division. The reminder is 32. The topmost line 00065 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 65.
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}