Evaluate
\frac{57}{37}\approx 1.540540541
Factor
\frac{3 \cdot 19}{37} = 1\frac{20}{37} = 1.5405405405405406
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\begin{array}{l}\phantom{555)}\phantom{1}\\555\overline{)855}\\\end{array}
Use the 1^{st} digit 8 from dividend 855
\begin{array}{l}\phantom{555)}0\phantom{2}\\555\overline{)855}\\\end{array}
Since 8 is less than 555, use the next digit 5 from dividend 855 and add 0 to the quotient
\begin{array}{l}\phantom{555)}0\phantom{3}\\555\overline{)855}\\\end{array}
Use the 2^{nd} digit 5 from dividend 855
\begin{array}{l}\phantom{555)}00\phantom{4}\\555\overline{)855}\\\end{array}
Since 85 is less than 555, use the next digit 5 from dividend 855 and add 0 to the quotient
\begin{array}{l}\phantom{555)}00\phantom{5}\\555\overline{)855}\\\end{array}
Use the 3^{rd} digit 5 from dividend 855
\begin{array}{l}\phantom{555)}001\phantom{6}\\555\overline{)855}\\\phantom{555)}\underline{\phantom{}555\phantom{}}\\\phantom{555)}300\\\end{array}
Find closest multiple of 555 to 855. We see that 1 \times 555 = 555 is the nearest. Now subtract 555 from 855 to get reminder 300. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }300
Since 300 is less than 555, stop the division. The reminder is 300. The topmost line 001 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}