Evaluate
\frac{75}{2}=37.5
Factor
\frac{3 \cdot 5 ^ {2}}{2} = 37\frac{1}{2} = 37.5
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)750}\\\end{array}
Use the 1^{st} digit 7 from dividend 750
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)750}\\\end{array}
Since 7 is less than 20, use the next digit 5 from dividend 750 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)750}\\\end{array}
Use the 2^{nd} digit 5 from dividend 750
\begin{array}{l}\phantom{20)}03\phantom{4}\\20\overline{)750}\\\phantom{20)}\underline{\phantom{}60\phantom{9}}\\\phantom{20)}15\\\end{array}
Find closest multiple of 20 to 75. We see that 3 \times 20 = 60 is the nearest. Now subtract 60 from 75 to get reminder 15. Add 3 to quotient.
\begin{array}{l}\phantom{20)}03\phantom{5}\\20\overline{)750}\\\phantom{20)}\underline{\phantom{}60\phantom{9}}\\\phantom{20)}150\\\end{array}
Use the 3^{rd} digit 0 from dividend 750
\begin{array}{l}\phantom{20)}037\phantom{6}\\20\overline{)750}\\\phantom{20)}\underline{\phantom{}60\phantom{9}}\\\phantom{20)}150\\\phantom{20)}\underline{\phantom{}140\phantom{}}\\\phantom{20)9}10\\\end{array}
Find closest multiple of 20 to 150. We see that 7 \times 20 = 140 is the nearest. Now subtract 140 from 150 to get reminder 10. Add 7 to quotient.
\text{Quotient: }37 \text{Reminder: }10
Since 10 is less than 20, stop the division. The reminder is 10. The topmost line 037 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 37.
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}