Evaluate
\frac{37}{23}\approx 1.608695652
Factor
\frac{37}{23} = 1\frac{14}{23} = 1.608695652173913
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)37}\\\end{array}
Use the 1^{st} digit 3 from dividend 37
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)37}\\\end{array}
Since 3 is less than 23, use the next digit 7 from dividend 37 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)37}\\\end{array}
Use the 2^{nd} digit 7 from dividend 37
\begin{array}{l}\phantom{23)}01\phantom{4}\\23\overline{)37}\\\phantom{23)}\underline{\phantom{}23\phantom{}}\\\phantom{23)}14\\\end{array}
Find closest multiple of 23 to 37. We see that 1 \times 23 = 23 is the nearest. Now subtract 23 from 37 to get reminder 14. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }14
Since 14 is less than 23, stop the division. The reminder is 14. 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}