Evaluate
8
Factor
2^{3}
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\begin{array}{l}\phantom{500)}\phantom{1}\\500\overline{)4000}\\\end{array}
Use the 1^{st} digit 4 from dividend 4000
\begin{array}{l}\phantom{500)}0\phantom{2}\\500\overline{)4000}\\\end{array}
Since 4 is less than 500, use the next digit 0 from dividend 4000 and add 0 to the quotient
\begin{array}{l}\phantom{500)}0\phantom{3}\\500\overline{)4000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 4000
\begin{array}{l}\phantom{500)}00\phantom{4}\\500\overline{)4000}\\\end{array}
Since 40 is less than 500, use the next digit 0 from dividend 4000 and add 0 to the quotient
\begin{array}{l}\phantom{500)}00\phantom{5}\\500\overline{)4000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 4000
\begin{array}{l}\phantom{500)}000\phantom{6}\\500\overline{)4000}\\\end{array}
Since 400 is less than 500, use the next digit 0 from dividend 4000 and add 0 to the quotient
\begin{array}{l}\phantom{500)}000\phantom{7}\\500\overline{)4000}\\\end{array}
Use the 4^{th} digit 0 from dividend 4000
\begin{array}{l}\phantom{500)}0008\phantom{8}\\500\overline{)4000}\\\phantom{500)}\underline{\phantom{}4000\phantom{}}\\\phantom{500)9999}0\\\end{array}
Find closest multiple of 500 to 4000. We see that 8 \times 500 = 4000 is the nearest. Now subtract 4000 from 4000 to get reminder 0. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }0
Since 0 is less than 500, stop the division. The reminder is 0. The topmost line 0008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}