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2
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\begin{array}{l}\phantom{500)}\phantom{1}\\500\overline{)1000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1000
\begin{array}{l}\phantom{500)}0\phantom{2}\\500\overline{)1000}\\\end{array}
Since 1 is less than 500, use the next digit 0 from dividend 1000 and add 0 to the quotient
\begin{array}{l}\phantom{500)}0\phantom{3}\\500\overline{)1000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1000
\begin{array}{l}\phantom{500)}00\phantom{4}\\500\overline{)1000}\\\end{array}
Since 10 is less than 500, use the next digit 0 from dividend 1000 and add 0 to the quotient
\begin{array}{l}\phantom{500)}00\phantom{5}\\500\overline{)1000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1000
\begin{array}{l}\phantom{500)}000\phantom{6}\\500\overline{)1000}\\\end{array}
Since 100 is less than 500, use the next digit 0 from dividend 1000 and add 0 to the quotient
\begin{array}{l}\phantom{500)}000\phantom{7}\\500\overline{)1000}\\\end{array}
Use the 4^{th} digit 0 from dividend 1000
\begin{array}{l}\phantom{500)}0002\phantom{8}\\500\overline{)1000}\\\phantom{500)}\underline{\phantom{}1000\phantom{}}\\\phantom{500)9999}0\\\end{array}
Find closest multiple of 500 to 1000. We see that 2 \times 500 = 1000 is the nearest. Now subtract 1000 from 1000 to get reminder 0. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }0
Since 0 is less than 500, stop the division. The reminder is 0. The topmost line 0002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}