Evaluate
\frac{25}{19}\approx 1.315789474
Factor
\frac{5 ^ {2}}{19} = 1\frac{6}{19} = 1.3157894736842106
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\begin{array}{l}\phantom{194560000)}\phantom{1}\\194560000\overline{)256000000}\\\end{array}
Use the 1^{st} digit 2 from dividend 256000000
\begin{array}{l}\phantom{194560000)}0\phantom{2}\\194560000\overline{)256000000}\\\end{array}
Since 2 is less than 194560000, use the next digit 5 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}0\phantom{3}\\194560000\overline{)256000000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 256000000
\begin{array}{l}\phantom{194560000)}00\phantom{4}\\194560000\overline{)256000000}\\\end{array}
Since 25 is less than 194560000, use the next digit 6 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}00\phantom{5}\\194560000\overline{)256000000}\\\end{array}
Use the 3^{rd} digit 6 from dividend 256000000
\begin{array}{l}\phantom{194560000)}000\phantom{6}\\194560000\overline{)256000000}\\\end{array}
Since 256 is less than 194560000, use the next digit 0 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}000\phantom{7}\\194560000\overline{)256000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 256000000
\begin{array}{l}\phantom{194560000)}0000\phantom{8}\\194560000\overline{)256000000}\\\end{array}
Since 2560 is less than 194560000, use the next digit 0 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}0000\phantom{9}\\194560000\overline{)256000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 256000000
\begin{array}{l}\phantom{194560000)}00000\phantom{10}\\194560000\overline{)256000000}\\\end{array}
Since 25600 is less than 194560000, use the next digit 0 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}00000\phantom{11}\\194560000\overline{)256000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 256000000
\begin{array}{l}\phantom{194560000)}000000\phantom{12}\\194560000\overline{)256000000}\\\end{array}
Since 256000 is less than 194560000, use the next digit 0 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}000000\phantom{13}\\194560000\overline{)256000000}\\\end{array}
Use the 7^{th} digit 0 from dividend 256000000
\begin{array}{l}\phantom{194560000)}0000000\phantom{14}\\194560000\overline{)256000000}\\\end{array}
Since 2560000 is less than 194560000, use the next digit 0 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}0000000\phantom{15}\\194560000\overline{)256000000}\\\end{array}
Use the 8^{th} digit 0 from dividend 256000000
\begin{array}{l}\phantom{194560000)}00000000\phantom{16}\\194560000\overline{)256000000}\\\end{array}
Since 25600000 is less than 194560000, use the next digit 0 from dividend 256000000 and add 0 to the quotient
\begin{array}{l}\phantom{194560000)}00000000\phantom{17}\\194560000\overline{)256000000}\\\end{array}
Use the 9^{th} digit 0 from dividend 256000000
\begin{array}{l}\phantom{194560000)}000000001\phantom{18}\\194560000\overline{)256000000}\\\phantom{194560000)}\underline{\phantom{}194560000\phantom{}}\\\phantom{194560000)9}61440000\\\end{array}
Find closest multiple of 194560000 to 256000000. We see that 1 \times 194560000 = 194560000 is the nearest. Now subtract 194560000 from 256000000 to get reminder 61440000. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }61440000
Since 61440000 is less than 194560000, stop the division. The reminder is 61440000. The topmost line 000000001 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}