Evaluate
\frac{1000}{9}\approx 111.111111111
Factor
\frac{2 ^ {3} \cdot 5 ^ {3}}{3 ^ {2}} = 111\frac{1}{9} = 111.11111111111111
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\begin{array}{l}\phantom{360)}\phantom{1}\\360\overline{)40000}\\\end{array}
Use the 1^{st} digit 4 from dividend 40000
\begin{array}{l}\phantom{360)}0\phantom{2}\\360\overline{)40000}\\\end{array}
Since 4 is less than 360, use the next digit 0 from dividend 40000 and add 0 to the quotient
\begin{array}{l}\phantom{360)}0\phantom{3}\\360\overline{)40000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 40000
\begin{array}{l}\phantom{360)}00\phantom{4}\\360\overline{)40000}\\\end{array}
Since 40 is less than 360, use the next digit 0 from dividend 40000 and add 0 to the quotient
\begin{array}{l}\phantom{360)}00\phantom{5}\\360\overline{)40000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 40000
\begin{array}{l}\phantom{360)}001\phantom{6}\\360\overline{)40000}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)9}40\\\end{array}
Find closest multiple of 360 to 400. We see that 1 \times 360 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 1 to quotient.
\begin{array}{l}\phantom{360)}001\phantom{7}\\360\overline{)40000}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)9}400\\\end{array}
Use the 4^{th} digit 0 from dividend 40000
\begin{array}{l}\phantom{360)}0011\phantom{8}\\360\overline{)40000}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)9}400\\\phantom{360)}\underline{\phantom{9}360\phantom{9}}\\\phantom{360)99}40\\\end{array}
Find closest multiple of 360 to 400. We see that 1 \times 360 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 1 to quotient.
\begin{array}{l}\phantom{360)}0011\phantom{9}\\360\overline{)40000}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)9}400\\\phantom{360)}\underline{\phantom{9}360\phantom{9}}\\\phantom{360)99}400\\\end{array}
Use the 5^{th} digit 0 from dividend 40000
\begin{array}{l}\phantom{360)}00111\phantom{10}\\360\overline{)40000}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)9}400\\\phantom{360)}\underline{\phantom{9}360\phantom{9}}\\\phantom{360)99}400\\\phantom{360)}\underline{\phantom{99}360\phantom{}}\\\phantom{360)999}40\\\end{array}
Find closest multiple of 360 to 400. We see that 1 \times 360 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 1 to quotient.
\text{Quotient: }111 \text{Reminder: }40
Since 40 is less than 360, stop the division. The reminder is 40. The topmost line 00111 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 111.
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}