Evaluate
\frac{109739369}{13717421}\approx 8.000000073
Factor
\frac{17 ^ {2} \cdot 379721}{3607 \cdot 3803} = 8\frac{1}{13717421} = 8.0000000729
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\begin{array}{l}\phantom{123456789)}\phantom{1}\\123456789\overline{)987654321}\\\end{array}
Use the 1^{st} digit 9 from dividend 987654321
\begin{array}{l}\phantom{123456789)}0\phantom{2}\\123456789\overline{)987654321}\\\end{array}
Since 9 is less than 123456789, use the next digit 8 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}0\phantom{3}\\123456789\overline{)987654321}\\\end{array}
Use the 2^{nd} digit 8 from dividend 987654321
\begin{array}{l}\phantom{123456789)}00\phantom{4}\\123456789\overline{)987654321}\\\end{array}
Since 98 is less than 123456789, use the next digit 7 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}00\phantom{5}\\123456789\overline{)987654321}\\\end{array}
Use the 3^{rd} digit 7 from dividend 987654321
\begin{array}{l}\phantom{123456789)}000\phantom{6}\\123456789\overline{)987654321}\\\end{array}
Since 987 is less than 123456789, use the next digit 6 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}000\phantom{7}\\123456789\overline{)987654321}\\\end{array}
Use the 4^{th} digit 6 from dividend 987654321
\begin{array}{l}\phantom{123456789)}0000\phantom{8}\\123456789\overline{)987654321}\\\end{array}
Since 9876 is less than 123456789, use the next digit 5 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}0000\phantom{9}\\123456789\overline{)987654321}\\\end{array}
Use the 5^{th} digit 5 from dividend 987654321
\begin{array}{l}\phantom{123456789)}00000\phantom{10}\\123456789\overline{)987654321}\\\end{array}
Since 98765 is less than 123456789, use the next digit 4 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}00000\phantom{11}\\123456789\overline{)987654321}\\\end{array}
Use the 6^{th} digit 4 from dividend 987654321
\begin{array}{l}\phantom{123456789)}000000\phantom{12}\\123456789\overline{)987654321}\\\end{array}
Since 987654 is less than 123456789, use the next digit 3 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}000000\phantom{13}\\123456789\overline{)987654321}\\\end{array}
Use the 7^{th} digit 3 from dividend 987654321
\begin{array}{l}\phantom{123456789)}0000000\phantom{14}\\123456789\overline{)987654321}\\\end{array}
Since 9876543 is less than 123456789, use the next digit 2 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}0000000\phantom{15}\\123456789\overline{)987654321}\\\end{array}
Use the 8^{th} digit 2 from dividend 987654321
\begin{array}{l}\phantom{123456789)}00000000\phantom{16}\\123456789\overline{)987654321}\\\end{array}
Since 98765432 is less than 123456789, use the next digit 1 from dividend 987654321 and add 0 to the quotient
\begin{array}{l}\phantom{123456789)}00000000\phantom{17}\\123456789\overline{)987654321}\\\end{array}
Use the 9^{th} digit 1 from dividend 987654321
\begin{array}{l}\phantom{123456789)}000000008\phantom{18}\\123456789\overline{)987654321}\\\phantom{123456789)}\underline{\phantom{}987654312\phantom{}}\\\phantom{123456789)99999999}9\\\end{array}
Find closest multiple of 123456789 to 987654321. We see that 8 \times 123456789 = 987654312 is the nearest. Now subtract 987654312 from 987654321 to get reminder 9. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }9
Since 9 is less than 123456789, stop the division. The reminder is 9. The topmost line 000000008 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}