Evaluate
\frac{225}{19}\approx 11.842105263
Factor
\frac{3 ^ {2} \cdot 5 ^ {2}}{19} = 11\frac{16}{19} = 11.842105263157896
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\begin{array}{l}\phantom{76000)}\phantom{1}\\76000\overline{)900000}\\\end{array}
Use the 1^{st} digit 9 from dividend 900000
\begin{array}{l}\phantom{76000)}0\phantom{2}\\76000\overline{)900000}\\\end{array}
Since 9 is less than 76000, use the next digit 0 from dividend 900000 and add 0 to the quotient
\begin{array}{l}\phantom{76000)}0\phantom{3}\\76000\overline{)900000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 900000
\begin{array}{l}\phantom{76000)}00\phantom{4}\\76000\overline{)900000}\\\end{array}
Since 90 is less than 76000, use the next digit 0 from dividend 900000 and add 0 to the quotient
\begin{array}{l}\phantom{76000)}00\phantom{5}\\76000\overline{)900000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 900000
\begin{array}{l}\phantom{76000)}000\phantom{6}\\76000\overline{)900000}\\\end{array}
Since 900 is less than 76000, use the next digit 0 from dividend 900000 and add 0 to the quotient
\begin{array}{l}\phantom{76000)}000\phantom{7}\\76000\overline{)900000}\\\end{array}
Use the 4^{th} digit 0 from dividend 900000
\begin{array}{l}\phantom{76000)}0000\phantom{8}\\76000\overline{)900000}\\\end{array}
Since 9000 is less than 76000, use the next digit 0 from dividend 900000 and add 0 to the quotient
\begin{array}{l}\phantom{76000)}0000\phantom{9}\\76000\overline{)900000}\\\end{array}
Use the 5^{th} digit 0 from dividend 900000
\begin{array}{l}\phantom{76000)}00001\phantom{10}\\76000\overline{)900000}\\\phantom{76000)}\underline{\phantom{}76000\phantom{9}}\\\phantom{76000)}14000\\\end{array}
Find closest multiple of 76000 to 90000. We see that 1 \times 76000 = 76000 is the nearest. Now subtract 76000 from 90000 to get reminder 14000. Add 1 to quotient.
\begin{array}{l}\phantom{76000)}00001\phantom{11}\\76000\overline{)900000}\\\phantom{76000)}\underline{\phantom{}76000\phantom{9}}\\\phantom{76000)}140000\\\end{array}
Use the 6^{th} digit 0 from dividend 900000
\begin{array}{l}\phantom{76000)}000011\phantom{12}\\76000\overline{)900000}\\\phantom{76000)}\underline{\phantom{}76000\phantom{9}}\\\phantom{76000)}140000\\\phantom{76000)}\underline{\phantom{9}76000\phantom{}}\\\phantom{76000)9}64000\\\end{array}
Find closest multiple of 76000 to 140000. We see that 1 \times 76000 = 76000 is the nearest. Now subtract 76000 from 140000 to get reminder 64000. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }64000
Since 64000 is less than 76000, stop the division. The reminder is 64000. The topmost line 000011 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}