Evaluate
\frac{9876543}{1234567}\approx 8.00000567
Factor
\frac{3 \cdot 227 \cdot 14503}{127 \cdot 9721} = 8\frac{7}{1234567} = 8.000005670004139
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\begin{array}{l}\phantom{1234567)}\phantom{1}\\1234567\overline{)9876543}\\\end{array}
Use the 1^{st} digit 9 from dividend 9876543
\begin{array}{l}\phantom{1234567)}0\phantom{2}\\1234567\overline{)9876543}\\\end{array}
Since 9 is less than 1234567, use the next digit 8 from dividend 9876543 and add 0 to the quotient
\begin{array}{l}\phantom{1234567)}0\phantom{3}\\1234567\overline{)9876543}\\\end{array}
Use the 2^{nd} digit 8 from dividend 9876543
\begin{array}{l}\phantom{1234567)}00\phantom{4}\\1234567\overline{)9876543}\\\end{array}
Since 98 is less than 1234567, use the next digit 7 from dividend 9876543 and add 0 to the quotient
\begin{array}{l}\phantom{1234567)}00\phantom{5}\\1234567\overline{)9876543}\\\end{array}
Use the 3^{rd} digit 7 from dividend 9876543
\begin{array}{l}\phantom{1234567)}000\phantom{6}\\1234567\overline{)9876543}\\\end{array}
Since 987 is less than 1234567, use the next digit 6 from dividend 9876543 and add 0 to the quotient
\begin{array}{l}\phantom{1234567)}000\phantom{7}\\1234567\overline{)9876543}\\\end{array}
Use the 4^{th} digit 6 from dividend 9876543
\begin{array}{l}\phantom{1234567)}0000\phantom{8}\\1234567\overline{)9876543}\\\end{array}
Since 9876 is less than 1234567, use the next digit 5 from dividend 9876543 and add 0 to the quotient
\begin{array}{l}\phantom{1234567)}0000\phantom{9}\\1234567\overline{)9876543}\\\end{array}
Use the 5^{th} digit 5 from dividend 9876543
\begin{array}{l}\phantom{1234567)}00000\phantom{10}\\1234567\overline{)9876543}\\\end{array}
Since 98765 is less than 1234567, use the next digit 4 from dividend 9876543 and add 0 to the quotient
\begin{array}{l}\phantom{1234567)}00000\phantom{11}\\1234567\overline{)9876543}\\\end{array}
Use the 6^{th} digit 4 from dividend 9876543
\begin{array}{l}\phantom{1234567)}000000\phantom{12}\\1234567\overline{)9876543}\\\end{array}
Since 987654 is less than 1234567, use the next digit 3 from dividend 9876543 and add 0 to the quotient
\begin{array}{l}\phantom{1234567)}000000\phantom{13}\\1234567\overline{)9876543}\\\end{array}
Use the 7^{th} digit 3 from dividend 9876543
\begin{array}{l}\phantom{1234567)}0000008\phantom{14}\\1234567\overline{)9876543}\\\phantom{1234567)}\underline{\phantom{}9876536\phantom{}}\\\phantom{1234567)999999}7\\\end{array}
Find closest multiple of 1234567 to 9876543. We see that 8 \times 1234567 = 9876536 is the nearest. Now subtract 9876536 from 9876543 to get reminder 7. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }7
Since 7 is less than 1234567, stop the division. The reminder is 7. The topmost line 0000008 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}