Evaluate
\frac{98765}{4321}\approx 22.856977551
Factor
\frac{5 \cdot 19753}{29 \cdot 149} = 22\frac{3703}{4321} = 22.85697755149271
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\begin{array}{l}\phantom{4321)}\phantom{1}\\4321\overline{)98765}\\\end{array}
Use the 1^{st} digit 9 from dividend 98765
\begin{array}{l}\phantom{4321)}0\phantom{2}\\4321\overline{)98765}\\\end{array}
Since 9 is less than 4321, use the next digit 8 from dividend 98765 and add 0 to the quotient
\begin{array}{l}\phantom{4321)}0\phantom{3}\\4321\overline{)98765}\\\end{array}
Use the 2^{nd} digit 8 from dividend 98765
\begin{array}{l}\phantom{4321)}00\phantom{4}\\4321\overline{)98765}\\\end{array}
Since 98 is less than 4321, use the next digit 7 from dividend 98765 and add 0 to the quotient
\begin{array}{l}\phantom{4321)}00\phantom{5}\\4321\overline{)98765}\\\end{array}
Use the 3^{rd} digit 7 from dividend 98765
\begin{array}{l}\phantom{4321)}000\phantom{6}\\4321\overline{)98765}\\\end{array}
Since 987 is less than 4321, use the next digit 6 from dividend 98765 and add 0 to the quotient
\begin{array}{l}\phantom{4321)}000\phantom{7}\\4321\overline{)98765}\\\end{array}
Use the 4^{th} digit 6 from dividend 98765
\begin{array}{l}\phantom{4321)}0002\phantom{8}\\4321\overline{)98765}\\\phantom{4321)}\underline{\phantom{}8642\phantom{9}}\\\phantom{4321)}1234\\\end{array}
Find closest multiple of 4321 to 9876. We see that 2 \times 4321 = 8642 is the nearest. Now subtract 8642 from 9876 to get reminder 1234. Add 2 to quotient.
\begin{array}{l}\phantom{4321)}0002\phantom{9}\\4321\overline{)98765}\\\phantom{4321)}\underline{\phantom{}8642\phantom{9}}\\\phantom{4321)}12345\\\end{array}
Use the 5^{th} digit 5 from dividend 98765
\begin{array}{l}\phantom{4321)}00022\phantom{10}\\4321\overline{)98765}\\\phantom{4321)}\underline{\phantom{}8642\phantom{9}}\\\phantom{4321)}12345\\\phantom{4321)}\underline{\phantom{9}8642\phantom{}}\\\phantom{4321)9}3703\\\end{array}
Find closest multiple of 4321 to 12345. We see that 2 \times 4321 = 8642 is the nearest. Now subtract 8642 from 12345 to get reminder 3703. Add 2 to quotient.
\text{Quotient: }22 \text{Reminder: }3703
Since 3703 is less than 4321, stop the division. The reminder is 3703. The topmost line 00022 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 22.
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}