Evaluate
\frac{220000}{3}\approx 73333.333333333
Factor
\frac{2 ^ {5} \cdot 5 ^ {4} \cdot 11}{3} = 73333\frac{1}{3} = 73333.33333333333
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)2200000}\\\end{array}
Use the 1^{st} digit 2 from dividend 2200000
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)2200000}\\\end{array}
Since 2 is less than 30, use the next digit 2 from dividend 2200000 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)2200000}\\\end{array}
Use the 2^{nd} digit 2 from dividend 2200000
\begin{array}{l}\phantom{30)}00\phantom{4}\\30\overline{)2200000}\\\end{array}
Since 22 is less than 30, use the next digit 0 from dividend 2200000 and add 0 to the quotient
\begin{array}{l}\phantom{30)}00\phantom{5}\\30\overline{)2200000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 2200000
\begin{array}{l}\phantom{30)}007\phantom{6}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}10\\\end{array}
Find closest multiple of 30 to 220. We see that 7 \times 30 = 210 is the nearest. Now subtract 210 from 220 to get reminder 10. Add 7 to quotient.
\begin{array}{l}\phantom{30)}007\phantom{7}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 2200000
\begin{array}{l}\phantom{30)}0073\phantom{8}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\phantom{30)}\underline{\phantom{99}90\phantom{999}}\\\phantom{30)99}10\\\end{array}
Find closest multiple of 30 to 100. We see that 3 \times 30 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 3 to quotient.
\begin{array}{l}\phantom{30)}0073\phantom{9}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\phantom{30)}\underline{\phantom{99}90\phantom{999}}\\\phantom{30)99}100\\\end{array}
Use the 5^{th} digit 0 from dividend 2200000
\begin{array}{l}\phantom{30)}00733\phantom{10}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\phantom{30)}\underline{\phantom{99}90\phantom{999}}\\\phantom{30)99}100\\\phantom{30)}\underline{\phantom{999}90\phantom{99}}\\\phantom{30)999}10\\\end{array}
Find closest multiple of 30 to 100. We see that 3 \times 30 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 3 to quotient.
\begin{array}{l}\phantom{30)}00733\phantom{11}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\phantom{30)}\underline{\phantom{99}90\phantom{999}}\\\phantom{30)99}100\\\phantom{30)}\underline{\phantom{999}90\phantom{99}}\\\phantom{30)999}100\\\end{array}
Use the 6^{th} digit 0 from dividend 2200000
\begin{array}{l}\phantom{30)}007333\phantom{12}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\phantom{30)}\underline{\phantom{99}90\phantom{999}}\\\phantom{30)99}100\\\phantom{30)}\underline{\phantom{999}90\phantom{99}}\\\phantom{30)999}100\\\phantom{30)}\underline{\phantom{9999}90\phantom{9}}\\\phantom{30)9999}10\\\end{array}
Find closest multiple of 30 to 100. We see that 3 \times 30 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 3 to quotient.
\begin{array}{l}\phantom{30)}007333\phantom{13}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\phantom{30)}\underline{\phantom{99}90\phantom{999}}\\\phantom{30)99}100\\\phantom{30)}\underline{\phantom{999}90\phantom{99}}\\\phantom{30)999}100\\\phantom{30)}\underline{\phantom{9999}90\phantom{9}}\\\phantom{30)9999}100\\\end{array}
Use the 7^{th} digit 0 from dividend 2200000
\begin{array}{l}\phantom{30)}0073333\phantom{14}\\30\overline{)2200000}\\\phantom{30)}\underline{\phantom{}210\phantom{9999}}\\\phantom{30)9}100\\\phantom{30)}\underline{\phantom{99}90\phantom{999}}\\\phantom{30)99}100\\\phantom{30)}\underline{\phantom{999}90\phantom{99}}\\\phantom{30)999}100\\\phantom{30)}\underline{\phantom{9999}90\phantom{9}}\\\phantom{30)9999}100\\\phantom{30)}\underline{\phantom{99999}90\phantom{}}\\\phantom{30)99999}10\\\end{array}
Find closest multiple of 30 to 100. We see that 3 \times 30 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 3 to quotient.
\text{Quotient: }73333 \text{Reminder: }10
Since 10 is less than 30, stop the division. The reminder is 10. The topmost line 0073333 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 73333.
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}