Evaluate
\frac{29000}{133}\approx 218.045112782
Factor
\frac{2 ^ {3} \cdot 5 ^ {3} \cdot 29}{7 \cdot 19} = 218\frac{6}{133} = 218.04511278195488
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\begin{array}{l}\phantom{665)}\phantom{1}\\665\overline{)145000}\\\end{array}
Use the 1^{st} digit 1 from dividend 145000
\begin{array}{l}\phantom{665)}0\phantom{2}\\665\overline{)145000}\\\end{array}
Since 1 is less than 665, use the next digit 4 from dividend 145000 and add 0 to the quotient
\begin{array}{l}\phantom{665)}0\phantom{3}\\665\overline{)145000}\\\end{array}
Use the 2^{nd} digit 4 from dividend 145000
\begin{array}{l}\phantom{665)}00\phantom{4}\\665\overline{)145000}\\\end{array}
Since 14 is less than 665, use the next digit 5 from dividend 145000 and add 0 to the quotient
\begin{array}{l}\phantom{665)}00\phantom{5}\\665\overline{)145000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 145000
\begin{array}{l}\phantom{665)}000\phantom{6}\\665\overline{)145000}\\\end{array}
Since 145 is less than 665, use the next digit 0 from dividend 145000 and add 0 to the quotient
\begin{array}{l}\phantom{665)}000\phantom{7}\\665\overline{)145000}\\\end{array}
Use the 4^{th} digit 0 from dividend 145000
\begin{array}{l}\phantom{665)}0002\phantom{8}\\665\overline{)145000}\\\phantom{665)}\underline{\phantom{}1330\phantom{99}}\\\phantom{665)9}120\\\end{array}
Find closest multiple of 665 to 1450. We see that 2 \times 665 = 1330 is the nearest. Now subtract 1330 from 1450 to get reminder 120. Add 2 to quotient.
\begin{array}{l}\phantom{665)}0002\phantom{9}\\665\overline{)145000}\\\phantom{665)}\underline{\phantom{}1330\phantom{99}}\\\phantom{665)9}1200\\\end{array}
Use the 5^{th} digit 0 from dividend 145000
\begin{array}{l}\phantom{665)}00021\phantom{10}\\665\overline{)145000}\\\phantom{665)}\underline{\phantom{}1330\phantom{99}}\\\phantom{665)9}1200\\\phantom{665)}\underline{\phantom{99}665\phantom{9}}\\\phantom{665)99}535\\\end{array}
Find closest multiple of 665 to 1200. We see that 1 \times 665 = 665 is the nearest. Now subtract 665 from 1200 to get reminder 535. Add 1 to quotient.
\begin{array}{l}\phantom{665)}00021\phantom{11}\\665\overline{)145000}\\\phantom{665)}\underline{\phantom{}1330\phantom{99}}\\\phantom{665)9}1200\\\phantom{665)}\underline{\phantom{99}665\phantom{9}}\\\phantom{665)99}5350\\\end{array}
Use the 6^{th} digit 0 from dividend 145000
\begin{array}{l}\phantom{665)}000218\phantom{12}\\665\overline{)145000}\\\phantom{665)}\underline{\phantom{}1330\phantom{99}}\\\phantom{665)9}1200\\\phantom{665)}\underline{\phantom{99}665\phantom{9}}\\\phantom{665)99}5350\\\phantom{665)}\underline{\phantom{99}5320\phantom{}}\\\phantom{665)9999}30\\\end{array}
Find closest multiple of 665 to 5350. We see that 8 \times 665 = 5320 is the nearest. Now subtract 5320 from 5350 to get reminder 30. Add 8 to quotient.
\text{Quotient: }218 \text{Reminder: }30
Since 30 is less than 665, stop the division. The reminder is 30. The topmost line 000218 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 218.
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}