Evaluate
\frac{164609}{20576}\approx 8.0000486
Factor
\frac{97 \cdot 1697}{2 ^ {5} \cdot 643} = 8\frac{1}{20576} = 8.000048600311041
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\begin{array}{l}\phantom{123456)}\phantom{1}\\123456\overline{)987654}\\\end{array}
Use the 1^{st} digit 9 from dividend 987654
\begin{array}{l}\phantom{123456)}0\phantom{2}\\123456\overline{)987654}\\\end{array}
Since 9 is less than 123456, use the next digit 8 from dividend 987654 and add 0 to the quotient
\begin{array}{l}\phantom{123456)}0\phantom{3}\\123456\overline{)987654}\\\end{array}
Use the 2^{nd} digit 8 from dividend 987654
\begin{array}{l}\phantom{123456)}00\phantom{4}\\123456\overline{)987654}\\\end{array}
Since 98 is less than 123456, use the next digit 7 from dividend 987654 and add 0 to the quotient
\begin{array}{l}\phantom{123456)}00\phantom{5}\\123456\overline{)987654}\\\end{array}
Use the 3^{rd} digit 7 from dividend 987654
\begin{array}{l}\phantom{123456)}000\phantom{6}\\123456\overline{)987654}\\\end{array}
Since 987 is less than 123456, use the next digit 6 from dividend 987654 and add 0 to the quotient
\begin{array}{l}\phantom{123456)}000\phantom{7}\\123456\overline{)987654}\\\end{array}
Use the 4^{th} digit 6 from dividend 987654
\begin{array}{l}\phantom{123456)}0000\phantom{8}\\123456\overline{)987654}\\\end{array}
Since 9876 is less than 123456, use the next digit 5 from dividend 987654 and add 0 to the quotient
\begin{array}{l}\phantom{123456)}0000\phantom{9}\\123456\overline{)987654}\\\end{array}
Use the 5^{th} digit 5 from dividend 987654
\begin{array}{l}\phantom{123456)}00000\phantom{10}\\123456\overline{)987654}\\\end{array}
Since 98765 is less than 123456, use the next digit 4 from dividend 987654 and add 0 to the quotient
\begin{array}{l}\phantom{123456)}00000\phantom{11}\\123456\overline{)987654}\\\end{array}
Use the 6^{th} digit 4 from dividend 987654
\begin{array}{l}\phantom{123456)}000008\phantom{12}\\123456\overline{)987654}\\\phantom{123456)}\underline{\phantom{}987648\phantom{}}\\\phantom{123456)99999}6\\\end{array}
Find closest multiple of 123456 to 987654. We see that 8 \times 123456 = 987648 is the nearest. Now subtract 987648 from 987654 to get reminder 6. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }6
Since 6 is less than 123456, stop the division. The reminder is 6. The topmost line 000008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}