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{95000)}\phantom{1}\\95000\overline{)125000}\\\end{array}
Use the 1^{st} digit 1 from dividend 125000
\begin{array}{l}\phantom{95000)}0\phantom{2}\\95000\overline{)125000}\\\end{array}
Since 1 is less than 95000, use the next digit 2 from dividend 125000 and add 0 to the quotient
\begin{array}{l}\phantom{95000)}0\phantom{3}\\95000\overline{)125000}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125000
\begin{array}{l}\phantom{95000)}00\phantom{4}\\95000\overline{)125000}\\\end{array}
Since 12 is less than 95000, use the next digit 5 from dividend 125000 and add 0 to the quotient
\begin{array}{l}\phantom{95000)}00\phantom{5}\\95000\overline{)125000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125000
\begin{array}{l}\phantom{95000)}000\phantom{6}\\95000\overline{)125000}\\\end{array}
Since 125 is less than 95000, use the next digit 0 from dividend 125000 and add 0 to the quotient
\begin{array}{l}\phantom{95000)}000\phantom{7}\\95000\overline{)125000}\\\end{array}
Use the 4^{th} digit 0 from dividend 125000
\begin{array}{l}\phantom{95000)}0000\phantom{8}\\95000\overline{)125000}\\\end{array}
Since 1250 is less than 95000, use the next digit 0 from dividend 125000 and add 0 to the quotient
\begin{array}{l}\phantom{95000)}0000\phantom{9}\\95000\overline{)125000}\\\end{array}
Use the 5^{th} digit 0 from dividend 125000
\begin{array}{l}\phantom{95000)}00000\phantom{10}\\95000\overline{)125000}\\\end{array}
Since 12500 is less than 95000, use the next digit 0 from dividend 125000 and add 0 to the quotient
\begin{array}{l}\phantom{95000)}00000\phantom{11}\\95000\overline{)125000}\\\end{array}
Use the 6^{th} digit 0 from dividend 125000
\begin{array}{l}\phantom{95000)}000001\phantom{12}\\95000\overline{)125000}\\\phantom{95000)}\underline{\phantom{9}95000\phantom{}}\\\phantom{95000)9}30000\\\end{array}
Find closest multiple of 95000 to 125000. We see that 1 \times 95000 = 95000 is the nearest. Now subtract 95000 from 125000 to get reminder 30000. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }30000
Since 30000 is less than 95000, stop the division. The reminder is 30000. 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}