Evaluate
\frac{6380}{3}\approx 2126.666666667
Factor
\frac{2 ^ {2} \cdot 5 \cdot 11 \cdot 29}{3} = 2126\frac{2}{3} = 2126.6666666666665
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)38280}\\\end{array}
Use the 1^{st} digit 3 from dividend 38280
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)38280}\\\end{array}
Since 3 is less than 18, use the next digit 8 from dividend 38280 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)38280}\\\end{array}
Use the 2^{nd} digit 8 from dividend 38280
\begin{array}{l}\phantom{18)}02\phantom{4}\\18\overline{)38280}\\\phantom{18)}\underline{\phantom{}36\phantom{999}}\\\phantom{18)9}2\\\end{array}
Find closest multiple of 18 to 38. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 38 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{18)}02\phantom{5}\\18\overline{)38280}\\\phantom{18)}\underline{\phantom{}36\phantom{999}}\\\phantom{18)9}22\\\end{array}
Use the 3^{rd} digit 2 from dividend 38280
\begin{array}{l}\phantom{18)}021\phantom{6}\\18\overline{)38280}\\\phantom{18)}\underline{\phantom{}36\phantom{999}}\\\phantom{18)9}22\\\phantom{18)}\underline{\phantom{9}18\phantom{99}}\\\phantom{18)99}4\\\end{array}
Find closest multiple of 18 to 22. We see that 1 \times 18 = 18 is the nearest. Now subtract 18 from 22 to get reminder 4. Add 1 to quotient.
\begin{array}{l}\phantom{18)}021\phantom{7}\\18\overline{)38280}\\\phantom{18)}\underline{\phantom{}36\phantom{999}}\\\phantom{18)9}22\\\phantom{18)}\underline{\phantom{9}18\phantom{99}}\\\phantom{18)99}48\\\end{array}
Use the 4^{th} digit 8 from dividend 38280
\begin{array}{l}\phantom{18)}0212\phantom{8}\\18\overline{)38280}\\\phantom{18)}\underline{\phantom{}36\phantom{999}}\\\phantom{18)9}22\\\phantom{18)}\underline{\phantom{9}18\phantom{99}}\\\phantom{18)99}48\\\phantom{18)}\underline{\phantom{99}36\phantom{9}}\\\phantom{18)99}12\\\end{array}
Find closest multiple of 18 to 48. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 48 to get reminder 12. Add 2 to quotient.
\begin{array}{l}\phantom{18)}0212\phantom{9}\\18\overline{)38280}\\\phantom{18)}\underline{\phantom{}36\phantom{999}}\\\phantom{18)9}22\\\phantom{18)}\underline{\phantom{9}18\phantom{99}}\\\phantom{18)99}48\\\phantom{18)}\underline{\phantom{99}36\phantom{9}}\\\phantom{18)99}120\\\end{array}
Use the 5^{th} digit 0 from dividend 38280
\begin{array}{l}\phantom{18)}02126\phantom{10}\\18\overline{)38280}\\\phantom{18)}\underline{\phantom{}36\phantom{999}}\\\phantom{18)9}22\\\phantom{18)}\underline{\phantom{9}18\phantom{99}}\\\phantom{18)99}48\\\phantom{18)}\underline{\phantom{99}36\phantom{9}}\\\phantom{18)99}120\\\phantom{18)}\underline{\phantom{99}108\phantom{}}\\\phantom{18)999}12\\\end{array}
Find closest multiple of 18 to 120. We see that 6 \times 18 = 108 is the nearest. Now subtract 108 from 120 to get reminder 12. Add 6 to quotient.
\text{Quotient: }2126 \text{Reminder: }12
Since 12 is less than 18, stop the division. The reminder is 12. The topmost line 02126 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2126.
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}