Evaluate
\frac{390115}{9}\approx 43346.111111111
Factor
\frac{5 \cdot 11 \cdot 41 \cdot 173}{3 ^ {2}} = 43346\frac{1}{9} = 43346.11111111111
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\begin{array}{l}\phantom{225)}\phantom{1}\\225\overline{)9752875}\\\end{array}
Use the 1^{st} digit 9 from dividend 9752875
\begin{array}{l}\phantom{225)}0\phantom{2}\\225\overline{)9752875}\\\end{array}
Since 9 is less than 225, use the next digit 7 from dividend 9752875 and add 0 to the quotient
\begin{array}{l}\phantom{225)}0\phantom{3}\\225\overline{)9752875}\\\end{array}
Use the 2^{nd} digit 7 from dividend 9752875
\begin{array}{l}\phantom{225)}00\phantom{4}\\225\overline{)9752875}\\\end{array}
Since 97 is less than 225, use the next digit 5 from dividend 9752875 and add 0 to the quotient
\begin{array}{l}\phantom{225)}00\phantom{5}\\225\overline{)9752875}\\\end{array}
Use the 3^{rd} digit 5 from dividend 9752875
\begin{array}{l}\phantom{225)}004\phantom{6}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}75\\\end{array}
Find closest multiple of 225 to 975. We see that 4 \times 225 = 900 is the nearest. Now subtract 900 from 975 to get reminder 75. Add 4 to quotient.
\begin{array}{l}\phantom{225)}004\phantom{7}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\end{array}
Use the 4^{th} digit 2 from dividend 9752875
\begin{array}{l}\phantom{225)}0043\phantom{8}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\phantom{225)}\underline{\phantom{9}675\phantom{999}}\\\phantom{225)99}77\\\end{array}
Find closest multiple of 225 to 752. We see that 3 \times 225 = 675 is the nearest. Now subtract 675 from 752 to get reminder 77. Add 3 to quotient.
\begin{array}{l}\phantom{225)}0043\phantom{9}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\phantom{225)}\underline{\phantom{9}675\phantom{999}}\\\phantom{225)99}778\\\end{array}
Use the 5^{th} digit 8 from dividend 9752875
\begin{array}{l}\phantom{225)}00433\phantom{10}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\phantom{225)}\underline{\phantom{9}675\phantom{999}}\\\phantom{225)99}778\\\phantom{225)}\underline{\phantom{99}675\phantom{99}}\\\phantom{225)99}103\\\end{array}
Find closest multiple of 225 to 778. We see that 3 \times 225 = 675 is the nearest. Now subtract 675 from 778 to get reminder 103. Add 3 to quotient.
\begin{array}{l}\phantom{225)}00433\phantom{11}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\phantom{225)}\underline{\phantom{9}675\phantom{999}}\\\phantom{225)99}778\\\phantom{225)}\underline{\phantom{99}675\phantom{99}}\\\phantom{225)99}1037\\\end{array}
Use the 6^{th} digit 7 from dividend 9752875
\begin{array}{l}\phantom{225)}004334\phantom{12}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\phantom{225)}\underline{\phantom{9}675\phantom{999}}\\\phantom{225)99}778\\\phantom{225)}\underline{\phantom{99}675\phantom{99}}\\\phantom{225)99}1037\\\phantom{225)}\underline{\phantom{999}900\phantom{9}}\\\phantom{225)999}137\\\end{array}
Find closest multiple of 225 to 1037. We see that 4 \times 225 = 900 is the nearest. Now subtract 900 from 1037 to get reminder 137. Add 4 to quotient.
\begin{array}{l}\phantom{225)}004334\phantom{13}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\phantom{225)}\underline{\phantom{9}675\phantom{999}}\\\phantom{225)99}778\\\phantom{225)}\underline{\phantom{99}675\phantom{99}}\\\phantom{225)99}1037\\\phantom{225)}\underline{\phantom{999}900\phantom{9}}\\\phantom{225)999}1375\\\end{array}
Use the 7^{th} digit 5 from dividend 9752875
\begin{array}{l}\phantom{225)}0043346\phantom{14}\\225\overline{)9752875}\\\phantom{225)}\underline{\phantom{}900\phantom{9999}}\\\phantom{225)9}752\\\phantom{225)}\underline{\phantom{9}675\phantom{999}}\\\phantom{225)99}778\\\phantom{225)}\underline{\phantom{99}675\phantom{99}}\\\phantom{225)99}1037\\\phantom{225)}\underline{\phantom{999}900\phantom{9}}\\\phantom{225)999}1375\\\phantom{225)}\underline{\phantom{999}1350\phantom{}}\\\phantom{225)99999}25\\\end{array}
Find closest multiple of 225 to 1375. We see that 6 \times 225 = 1350 is the nearest. Now subtract 1350 from 1375 to get reminder 25. Add 6 to quotient.
\text{Quotient: }43346 \text{Reminder: }25
Since 25 is less than 225, stop the division. The reminder is 25. The topmost line 0043346 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 43346.
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}