Evaluate
\frac{107806}{106717}\approx 1.01020456
Factor
\frac{2 \cdot 19 \cdot 2837}{13 \cdot 8209} = 1\frac{1089}{106717} = 1.0102045597233806
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\begin{array}{l}\phantom{213434)}\phantom{1}\\213434\overline{)215612}\\\end{array}
Use the 1^{st} digit 2 from dividend 215612
\begin{array}{l}\phantom{213434)}0\phantom{2}\\213434\overline{)215612}\\\end{array}
Since 2 is less than 213434, use the next digit 1 from dividend 215612 and add 0 to the quotient
\begin{array}{l}\phantom{213434)}0\phantom{3}\\213434\overline{)215612}\\\end{array}
Use the 2^{nd} digit 1 from dividend 215612
\begin{array}{l}\phantom{213434)}00\phantom{4}\\213434\overline{)215612}\\\end{array}
Since 21 is less than 213434, use the next digit 5 from dividend 215612 and add 0 to the quotient
\begin{array}{l}\phantom{213434)}00\phantom{5}\\213434\overline{)215612}\\\end{array}
Use the 3^{rd} digit 5 from dividend 215612
\begin{array}{l}\phantom{213434)}000\phantom{6}\\213434\overline{)215612}\\\end{array}
Since 215 is less than 213434, use the next digit 6 from dividend 215612 and add 0 to the quotient
\begin{array}{l}\phantom{213434)}000\phantom{7}\\213434\overline{)215612}\\\end{array}
Use the 4^{th} digit 6 from dividend 215612
\begin{array}{l}\phantom{213434)}0000\phantom{8}\\213434\overline{)215612}\\\end{array}
Since 2156 is less than 213434, use the next digit 1 from dividend 215612 and add 0 to the quotient
\begin{array}{l}\phantom{213434)}0000\phantom{9}\\213434\overline{)215612}\\\end{array}
Use the 5^{th} digit 1 from dividend 215612
\begin{array}{l}\phantom{213434)}00000\phantom{10}\\213434\overline{)215612}\\\end{array}
Since 21561 is less than 213434, use the next digit 2 from dividend 215612 and add 0 to the quotient
\begin{array}{l}\phantom{213434)}00000\phantom{11}\\213434\overline{)215612}\\\end{array}
Use the 6^{th} digit 2 from dividend 215612
\begin{array}{l}\phantom{213434)}000001\phantom{12}\\213434\overline{)215612}\\\phantom{213434)}\underline{\phantom{}213434\phantom{}}\\\phantom{213434)99}2178\\\end{array}
Find closest multiple of 213434 to 215612. We see that 1 \times 213434 = 213434 is the nearest. Now subtract 213434 from 215612 to get reminder 2178. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }2178
Since 2178 is less than 213434, stop the division. The reminder is 2178. The topmost line 000001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}