Evaluate
\frac{2119}{5}=423.8
Factor
\frac{13 \cdot 163}{5} = 423\frac{4}{5} = 423.8
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)4238}\\\end{array}
Use the 1^{st} digit 4 from dividend 4238
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)4238}\\\end{array}
Since 4 is less than 10, use the next digit 2 from dividend 4238 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)4238}\\\end{array}
Use the 2^{nd} digit 2 from dividend 4238
\begin{array}{l}\phantom{10)}04\phantom{4}\\10\overline{)4238}\\\phantom{10)}\underline{\phantom{}40\phantom{99}}\\\phantom{10)9}2\\\end{array}
Find closest multiple of 10 to 42. We see that 4 \times 10 = 40 is the nearest. Now subtract 40 from 42 to get reminder 2. Add 4 to quotient.
\begin{array}{l}\phantom{10)}04\phantom{5}\\10\overline{)4238}\\\phantom{10)}\underline{\phantom{}40\phantom{99}}\\\phantom{10)9}23\\\end{array}
Use the 3^{rd} digit 3 from dividend 4238
\begin{array}{l}\phantom{10)}042\phantom{6}\\10\overline{)4238}\\\phantom{10)}\underline{\phantom{}40\phantom{99}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9}}\\\phantom{10)99}3\\\end{array}
Find closest multiple of 10 to 23. We see that 2 \times 10 = 20 is the nearest. Now subtract 20 from 23 to get reminder 3. Add 2 to quotient.
\begin{array}{l}\phantom{10)}042\phantom{7}\\10\overline{)4238}\\\phantom{10)}\underline{\phantom{}40\phantom{99}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9}}\\\phantom{10)99}38\\\end{array}
Use the 4^{th} digit 8 from dividend 4238
\begin{array}{l}\phantom{10)}0423\phantom{8}\\10\overline{)4238}\\\phantom{10)}\underline{\phantom{}40\phantom{99}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9}}\\\phantom{10)99}38\\\phantom{10)}\underline{\phantom{99}30\phantom{}}\\\phantom{10)999}8\\\end{array}
Find closest multiple of 10 to 38. We see that 3 \times 10 = 30 is the nearest. Now subtract 30 from 38 to get reminder 8. Add 3 to quotient.
\text{Quotient: }423 \text{Reminder: }8
Since 8 is less than 10, stop the division. The reminder is 8. The topmost line 0423 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 423.
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}