Evaluate
\frac{500}{21}\approx 23.80952381
Factor
\frac{2 ^ {2} \cdot 5 ^ {3}}{3 \cdot 7} = 23\frac{17}{21} = 23.80952380952381
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\begin{array}{l}\phantom{42000)}\phantom{1}\\42000\overline{)1000000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1000000
\begin{array}{l}\phantom{42000)}0\phantom{2}\\42000\overline{)1000000}\\\end{array}
Since 1 is less than 42000, use the next digit 0 from dividend 1000000 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}0\phantom{3}\\42000\overline{)1000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1000000
\begin{array}{l}\phantom{42000)}00\phantom{4}\\42000\overline{)1000000}\\\end{array}
Since 10 is less than 42000, use the next digit 0 from dividend 1000000 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}00\phantom{5}\\42000\overline{)1000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1000000
\begin{array}{l}\phantom{42000)}000\phantom{6}\\42000\overline{)1000000}\\\end{array}
Since 100 is less than 42000, use the next digit 0 from dividend 1000000 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}000\phantom{7}\\42000\overline{)1000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{42000)}0000\phantom{8}\\42000\overline{)1000000}\\\end{array}
Since 1000 is less than 42000, use the next digit 0 from dividend 1000000 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}0000\phantom{9}\\42000\overline{)1000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{42000)}00000\phantom{10}\\42000\overline{)1000000}\\\end{array}
Since 10000 is less than 42000, use the next digit 0 from dividend 1000000 and add 0 to the quotient
\begin{array}{l}\phantom{42000)}00000\phantom{11}\\42000\overline{)1000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{42000)}000002\phantom{12}\\42000\overline{)1000000}\\\phantom{42000)}\underline{\phantom{9}84000\phantom{9}}\\\phantom{42000)9}16000\\\end{array}
Find closest multiple of 42000 to 100000. We see that 2 \times 42000 = 84000 is the nearest. Now subtract 84000 from 100000 to get reminder 16000. Add 2 to quotient.
\begin{array}{l}\phantom{42000)}000002\phantom{13}\\42000\overline{)1000000}\\\phantom{42000)}\underline{\phantom{9}84000\phantom{9}}\\\phantom{42000)9}160000\\\end{array}
Use the 7^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{42000)}0000023\phantom{14}\\42000\overline{)1000000}\\\phantom{42000)}\underline{\phantom{9}84000\phantom{9}}\\\phantom{42000)9}160000\\\phantom{42000)}\underline{\phantom{9}126000\phantom{}}\\\phantom{42000)99}34000\\\end{array}
Find closest multiple of 42000 to 160000. We see that 3 \times 42000 = 126000 is the nearest. Now subtract 126000 from 160000 to get reminder 34000. Add 3 to quotient.
\text{Quotient: }23 \text{Reminder: }34000
Since 34000 is less than 42000, stop the division. The reminder is 34000. The topmost line 0000023 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 23.
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}