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{37)}\phantom{1}\\37\overline{)57}\\\end{array}
Use the 1^{st} digit 5 from dividend 57
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)57}\\\end{array}
Since 5 is less than 37, use the next digit 7 from dividend 57 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)57}\\\end{array}
Use the 2^{nd} digit 7 from dividend 57
\begin{array}{l}\phantom{37)}01\phantom{4}\\37\overline{)57}\\\phantom{37)}\underline{\phantom{}37\phantom{}}\\\phantom{37)}20\\\end{array}
Find closest multiple of 37 to 57. We see that 1 \times 37 = 37 is the nearest. Now subtract 37 from 57 to get reminder 20. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }20
Since 20 is less than 37, stop the division. The reminder is 20. The topmost line 01 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}