Evaluate
\frac{100}{9}\approx 11.111111111
Factor
\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {2}} = 11\frac{1}{9} = 11.11111111111111
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\begin{array}{l}\phantom{144000)}\phantom{1}\\144000\overline{)1600000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1600000
\begin{array}{l}\phantom{144000)}0\phantom{2}\\144000\overline{)1600000}\\\end{array}
Since 1 is less than 144000, use the next digit 6 from dividend 1600000 and add 0 to the quotient
\begin{array}{l}\phantom{144000)}0\phantom{3}\\144000\overline{)1600000}\\\end{array}
Use the 2^{nd} digit 6 from dividend 1600000
\begin{array}{l}\phantom{144000)}00\phantom{4}\\144000\overline{)1600000}\\\end{array}
Since 16 is less than 144000, use the next digit 0 from dividend 1600000 and add 0 to the quotient
\begin{array}{l}\phantom{144000)}00\phantom{5}\\144000\overline{)1600000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1600000
\begin{array}{l}\phantom{144000)}000\phantom{6}\\144000\overline{)1600000}\\\end{array}
Since 160 is less than 144000, use the next digit 0 from dividend 1600000 and add 0 to the quotient
\begin{array}{l}\phantom{144000)}000\phantom{7}\\144000\overline{)1600000}\\\end{array}
Use the 4^{th} digit 0 from dividend 1600000
\begin{array}{l}\phantom{144000)}0000\phantom{8}\\144000\overline{)1600000}\\\end{array}
Since 1600 is less than 144000, use the next digit 0 from dividend 1600000 and add 0 to the quotient
\begin{array}{l}\phantom{144000)}0000\phantom{9}\\144000\overline{)1600000}\\\end{array}
Use the 5^{th} digit 0 from dividend 1600000
\begin{array}{l}\phantom{144000)}00000\phantom{10}\\144000\overline{)1600000}\\\end{array}
Since 16000 is less than 144000, use the next digit 0 from dividend 1600000 and add 0 to the quotient
\begin{array}{l}\phantom{144000)}00000\phantom{11}\\144000\overline{)1600000}\\\end{array}
Use the 6^{th} digit 0 from dividend 1600000
\begin{array}{l}\phantom{144000)}000001\phantom{12}\\144000\overline{)1600000}\\\phantom{144000)}\underline{\phantom{}144000\phantom{9}}\\\phantom{144000)9}16000\\\end{array}
Find closest multiple of 144000 to 160000. We see that 1 \times 144000 = 144000 is the nearest. Now subtract 144000 from 160000 to get reminder 16000. Add 1 to quotient.
\begin{array}{l}\phantom{144000)}000001\phantom{13}\\144000\overline{)1600000}\\\phantom{144000)}\underline{\phantom{}144000\phantom{9}}\\\phantom{144000)9}160000\\\end{array}
Use the 7^{th} digit 0 from dividend 1600000
\begin{array}{l}\phantom{144000)}0000011\phantom{14}\\144000\overline{)1600000}\\\phantom{144000)}\underline{\phantom{}144000\phantom{9}}\\\phantom{144000)9}160000\\\phantom{144000)}\underline{\phantom{9}144000\phantom{}}\\\phantom{144000)99}16000\\\end{array}
Find closest multiple of 144000 to 160000. We see that 1 \times 144000 = 144000 is the nearest. Now subtract 144000 from 160000 to get reminder 16000. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }16000
Since 16000 is less than 144000, stop the division. The reminder is 16000. The topmost line 0000011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}