Evaluate
\frac{65000}{9}\approx 7222.222222222
Factor
\frac{2 ^ {3} \cdot 5 ^ {4} \cdot 13}{3 ^ {2}} = 7222\frac{2}{9} = 7222.222222222223
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)130000}\\\end{array}
Use the 1^{st} digit 1 from dividend 130000
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)130000}\\\end{array}
Since 1 is less than 18, use the next digit 3 from dividend 130000 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)130000}\\\end{array}
Use the 2^{nd} digit 3 from dividend 130000
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)130000}\\\end{array}
Since 13 is less than 18, use the next digit 0 from dividend 130000 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)130000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 130000
\begin{array}{l}\phantom{18)}007\phantom{6}\\18\overline{)130000}\\\phantom{18)}\underline{\phantom{}126\phantom{999}}\\\phantom{18)99}4\\\end{array}
Find closest multiple of 18 to 130. We see that 7 \times 18 = 126 is the nearest. Now subtract 126 from 130 to get reminder 4. Add 7 to quotient.
\begin{array}{l}\phantom{18)}007\phantom{7}\\18\overline{)130000}\\\phantom{18)}\underline{\phantom{}126\phantom{999}}\\\phantom{18)99}40\\\end{array}
Use the 4^{th} digit 0 from dividend 130000
\begin{array}{l}\phantom{18)}0072\phantom{8}\\18\overline{)130000}\\\phantom{18)}\underline{\phantom{}126\phantom{999}}\\\phantom{18)99}40\\\phantom{18)}\underline{\phantom{99}36\phantom{99}}\\\phantom{18)999}4\\\end{array}
Find closest multiple of 18 to 40. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 40 to get reminder 4. Add 2 to quotient.
\begin{array}{l}\phantom{18)}0072\phantom{9}\\18\overline{)130000}\\\phantom{18)}\underline{\phantom{}126\phantom{999}}\\\phantom{18)99}40\\\phantom{18)}\underline{\phantom{99}36\phantom{99}}\\\phantom{18)999}40\\\end{array}
Use the 5^{th} digit 0 from dividend 130000
\begin{array}{l}\phantom{18)}00722\phantom{10}\\18\overline{)130000}\\\phantom{18)}\underline{\phantom{}126\phantom{999}}\\\phantom{18)99}40\\\phantom{18)}\underline{\phantom{99}36\phantom{99}}\\\phantom{18)999}40\\\phantom{18)}\underline{\phantom{999}36\phantom{9}}\\\phantom{18)9999}4\\\end{array}
Find closest multiple of 18 to 40. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 40 to get reminder 4. Add 2 to quotient.
\begin{array}{l}\phantom{18)}00722\phantom{11}\\18\overline{)130000}\\\phantom{18)}\underline{\phantom{}126\phantom{999}}\\\phantom{18)99}40\\\phantom{18)}\underline{\phantom{99}36\phantom{99}}\\\phantom{18)999}40\\\phantom{18)}\underline{\phantom{999}36\phantom{9}}\\\phantom{18)9999}40\\\end{array}
Use the 6^{th} digit 0 from dividend 130000
\begin{array}{l}\phantom{18)}007222\phantom{12}\\18\overline{)130000}\\\phantom{18)}\underline{\phantom{}126\phantom{999}}\\\phantom{18)99}40\\\phantom{18)}\underline{\phantom{99}36\phantom{99}}\\\phantom{18)999}40\\\phantom{18)}\underline{\phantom{999}36\phantom{9}}\\\phantom{18)9999}40\\\phantom{18)}\underline{\phantom{9999}36\phantom{}}\\\phantom{18)99999}4\\\end{array}
Find closest multiple of 18 to 40. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 40 to get reminder 4. Add 2 to quotient.
\text{Quotient: }7222 \text{Reminder: }4
Since 4 is less than 18, stop the division. The reminder is 4. The topmost line 007222 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7222.
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}