Evaluate
\frac{37}{4}=9.25
Factor
\frac{37}{2 ^ {2}} = 9\frac{1}{4} = 9.25
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\begin{array}{l}\phantom{68)}\phantom{1}\\68\overline{)629}\\\end{array}
Use the 1^{st} digit 6 from dividend 629
\begin{array}{l}\phantom{68)}0\phantom{2}\\68\overline{)629}\\\end{array}
Since 6 is less than 68, use the next digit 2 from dividend 629 and add 0 to the quotient
\begin{array}{l}\phantom{68)}0\phantom{3}\\68\overline{)629}\\\end{array}
Use the 2^{nd} digit 2 from dividend 629
\begin{array}{l}\phantom{68)}00\phantom{4}\\68\overline{)629}\\\end{array}
Since 62 is less than 68, use the next digit 9 from dividend 629 and add 0 to the quotient
\begin{array}{l}\phantom{68)}00\phantom{5}\\68\overline{)629}\\\end{array}
Use the 3^{rd} digit 9 from dividend 629
\begin{array}{l}\phantom{68)}009\phantom{6}\\68\overline{)629}\\\phantom{68)}\underline{\phantom{}612\phantom{}}\\\phantom{68)9}17\\\end{array}
Find closest multiple of 68 to 629. We see that 9 \times 68 = 612 is the nearest. Now subtract 612 from 629 to get reminder 17. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }17
Since 17 is less than 68, stop the division. The reminder is 17. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}