Evaluate
\frac{37500}{11}\approx 3409.090909091
Factor
\frac{2 ^ {2} \cdot 3 \cdot 5 ^ {5}}{11} = 3409\frac{1}{11} = 3409.090909090909
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\begin{array}{l}\phantom{44000)}\phantom{1}\\44000\overline{)150000000}\\\end{array}
Use the 1^{st} digit 1 from dividend 150000000
\begin{array}{l}\phantom{44000)}0\phantom{2}\\44000\overline{)150000000}\\\end{array}
Since 1 is less than 44000, use the next digit 5 from dividend 150000000 and add 0 to the quotient
\begin{array}{l}\phantom{44000)}0\phantom{3}\\44000\overline{)150000000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 150000000
\begin{array}{l}\phantom{44000)}00\phantom{4}\\44000\overline{)150000000}\\\end{array}
Since 15 is less than 44000, use the next digit 0 from dividend 150000000 and add 0 to the quotient
\begin{array}{l}\phantom{44000)}00\phantom{5}\\44000\overline{)150000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 150000000
\begin{array}{l}\phantom{44000)}000\phantom{6}\\44000\overline{)150000000}\\\end{array}
Since 150 is less than 44000, use the next digit 0 from dividend 150000000 and add 0 to the quotient
\begin{array}{l}\phantom{44000)}000\phantom{7}\\44000\overline{)150000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 150000000
\begin{array}{l}\phantom{44000)}0000\phantom{8}\\44000\overline{)150000000}\\\end{array}
Since 1500 is less than 44000, use the next digit 0 from dividend 150000000 and add 0 to the quotient
\begin{array}{l}\phantom{44000)}0000\phantom{9}\\44000\overline{)150000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 150000000
\begin{array}{l}\phantom{44000)}00000\phantom{10}\\44000\overline{)150000000}\\\end{array}
Since 15000 is less than 44000, use the next digit 0 from dividend 150000000 and add 0 to the quotient
\begin{array}{l}\phantom{44000)}00000\phantom{11}\\44000\overline{)150000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 150000000
\begin{array}{l}\phantom{44000)}000003\phantom{12}\\44000\overline{)150000000}\\\phantom{44000)}\underline{\phantom{}132000\phantom{999}}\\\phantom{44000)9}18000\\\end{array}
Find closest multiple of 44000 to 150000. We see that 3 \times 44000 = 132000 is the nearest. Now subtract 132000 from 150000 to get reminder 18000. Add 3 to quotient.
\begin{array}{l}\phantom{44000)}000003\phantom{13}\\44000\overline{)150000000}\\\phantom{44000)}\underline{\phantom{}132000\phantom{999}}\\\phantom{44000)9}180000\\\end{array}
Use the 7^{th} digit 0 from dividend 150000000
\begin{array}{l}\phantom{44000)}0000034\phantom{14}\\44000\overline{)150000000}\\\phantom{44000)}\underline{\phantom{}132000\phantom{999}}\\\phantom{44000)9}180000\\\phantom{44000)}\underline{\phantom{9}176000\phantom{99}}\\\phantom{44000)999}4000\\\end{array}
Find closest multiple of 44000 to 180000. We see that 4 \times 44000 = 176000 is the nearest. Now subtract 176000 from 180000 to get reminder 4000. Add 4 to quotient.
\begin{array}{l}\phantom{44000)}0000034\phantom{15}\\44000\overline{)150000000}\\\phantom{44000)}\underline{\phantom{}132000\phantom{999}}\\\phantom{44000)9}180000\\\phantom{44000)}\underline{\phantom{9}176000\phantom{99}}\\\phantom{44000)999}40000\\\end{array}
Use the 8^{th} digit 0 from dividend 150000000
\begin{array}{l}\phantom{44000)}00000340\phantom{16}\\44000\overline{)150000000}\\\phantom{44000)}\underline{\phantom{}132000\phantom{999}}\\\phantom{44000)9}180000\\\phantom{44000)}\underline{\phantom{9}176000\phantom{99}}\\\phantom{44000)999}40000\\\end{array}
Since 40000 is less than 44000, use the next digit 0 from dividend 150000000 and add 0 to the quotient
\begin{array}{l}\phantom{44000)}00000340\phantom{17}\\44000\overline{)150000000}\\\phantom{44000)}\underline{\phantom{}132000\phantom{999}}\\\phantom{44000)9}180000\\\phantom{44000)}\underline{\phantom{9}176000\phantom{99}}\\\phantom{44000)999}400000\\\end{array}
Use the 9^{th} digit 0 from dividend 150000000
\begin{array}{l}\phantom{44000)}000003409\phantom{18}\\44000\overline{)150000000}\\\phantom{44000)}\underline{\phantom{}132000\phantom{999}}\\\phantom{44000)9}180000\\\phantom{44000)}\underline{\phantom{9}176000\phantom{99}}\\\phantom{44000)999}400000\\\phantom{44000)}\underline{\phantom{999}396000\phantom{}}\\\phantom{44000)99999}4000\\\end{array}
Find closest multiple of 44000 to 400000. We see that 9 \times 44000 = 396000 is the nearest. Now subtract 396000 from 400000 to get reminder 4000. Add 9 to quotient.
\text{Quotient: }3409 \text{Reminder: }4000
Since 4000 is less than 44000, stop the division. The reminder is 4000. The topmost line 000003409 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3409.
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}