Evaluate
\frac{37}{19}\approx 1.947368421
Factor
\frac{37}{19} = 1\frac{18}{19} = 1.9473684210526316
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\begin{array}{l}\phantom{19)}\phantom{1}\\19\overline{)37}\\\end{array}
Use the 1^{st} digit 3 from dividend 37
\begin{array}{l}\phantom{19)}0\phantom{2}\\19\overline{)37}\\\end{array}
Since 3 is less than 19, use the next digit 7 from dividend 37 and add 0 to the quotient
\begin{array}{l}\phantom{19)}0\phantom{3}\\19\overline{)37}\\\end{array}
Use the 2^{nd} digit 7 from dividend 37
\begin{array}{l}\phantom{19)}01\phantom{4}\\19\overline{)37}\\\phantom{19)}\underline{\phantom{}19\phantom{}}\\\phantom{19)}18\\\end{array}
Find closest multiple of 19 to 37. We see that 1 \times 19 = 19 is the nearest. Now subtract 19 from 37 to get reminder 18. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }18
Since 18 is less than 19, stop the division. The reminder is 18. 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}