Evaluate
\frac{75000}{1777}\approx 42.20596511
Factor
\frac{2 ^ {3} \cdot 3 \cdot 5 ^ {5}}{1777} = 42\frac{366}{1777} = 42.20596510973551
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\begin{array}{l}\phantom{710800)}\phantom{1}\\710800\overline{)30000000}\\\end{array}
Use the 1^{st} digit 3 from dividend 30000000
\begin{array}{l}\phantom{710800)}0\phantom{2}\\710800\overline{)30000000}\\\end{array}
Since 3 is less than 710800, use the next digit 0 from dividend 30000000 and add 0 to the quotient
\begin{array}{l}\phantom{710800)}0\phantom{3}\\710800\overline{)30000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 30000000
\begin{array}{l}\phantom{710800)}00\phantom{4}\\710800\overline{)30000000}\\\end{array}
Since 30 is less than 710800, use the next digit 0 from dividend 30000000 and add 0 to the quotient
\begin{array}{l}\phantom{710800)}00\phantom{5}\\710800\overline{)30000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 30000000
\begin{array}{l}\phantom{710800)}000\phantom{6}\\710800\overline{)30000000}\\\end{array}
Since 300 is less than 710800, use the next digit 0 from dividend 30000000 and add 0 to the quotient
\begin{array}{l}\phantom{710800)}000\phantom{7}\\710800\overline{)30000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 30000000
\begin{array}{l}\phantom{710800)}0000\phantom{8}\\710800\overline{)30000000}\\\end{array}
Since 3000 is less than 710800, use the next digit 0 from dividend 30000000 and add 0 to the quotient
\begin{array}{l}\phantom{710800)}0000\phantom{9}\\710800\overline{)30000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 30000000
\begin{array}{l}\phantom{710800)}00000\phantom{10}\\710800\overline{)30000000}\\\end{array}
Since 30000 is less than 710800, use the next digit 0 from dividend 30000000 and add 0 to the quotient
\begin{array}{l}\phantom{710800)}00000\phantom{11}\\710800\overline{)30000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 30000000
\begin{array}{l}\phantom{710800)}000000\phantom{12}\\710800\overline{)30000000}\\\end{array}
Since 300000 is less than 710800, use the next digit 0 from dividend 30000000 and add 0 to the quotient
\begin{array}{l}\phantom{710800)}000000\phantom{13}\\710800\overline{)30000000}\\\end{array}
Use the 7^{th} digit 0 from dividend 30000000
\begin{array}{l}\phantom{710800)}0000004\phantom{14}\\710800\overline{)30000000}\\\phantom{710800)}\underline{\phantom{}2843200\phantom{9}}\\\phantom{710800)9}156800\\\end{array}
Find closest multiple of 710800 to 3000000. We see that 4 \times 710800 = 2843200 is the nearest. Now subtract 2843200 from 3000000 to get reminder 156800. Add 4 to quotient.
\begin{array}{l}\phantom{710800)}0000004\phantom{15}\\710800\overline{)30000000}\\\phantom{710800)}\underline{\phantom{}2843200\phantom{9}}\\\phantom{710800)9}1568000\\\end{array}
Use the 8^{th} digit 0 from dividend 30000000
\begin{array}{l}\phantom{710800)}00000042\phantom{16}\\710800\overline{)30000000}\\\phantom{710800)}\underline{\phantom{}2843200\phantom{9}}\\\phantom{710800)9}1568000\\\phantom{710800)}\underline{\phantom{9}1421600\phantom{}}\\\phantom{710800)99}146400\\\end{array}
Find closest multiple of 710800 to 1568000. We see that 2 \times 710800 = 1421600 is the nearest. Now subtract 1421600 from 1568000 to get reminder 146400. Add 2 to quotient.
\text{Quotient: }42 \text{Reminder: }146400
Since 146400 is less than 710800, stop the division. The reminder is 146400. The topmost line 00000042 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 42.
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}