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\begin{array}{l}\phantom{37)}\phantom{1}\\37\overline{)74}\\\end{array}
Use the 1^{st} digit 7 from dividend 74
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)74}\\\end{array}
Since 7 is less than 37, use the next digit 4 from dividend 74 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)74}\\\end{array}
Use the 2^{nd} digit 4 from dividend 74
\begin{array}{l}\phantom{37)}02\phantom{4}\\37\overline{)74}\\\phantom{37)}\underline{\phantom{}74\phantom{}}\\\phantom{37)99}0\\\end{array}
Find closest multiple of 37 to 74. We see that 2 \times 37 = 74 is the nearest. Now subtract 74 from 74 to get reminder 0. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }0
Since 0 is less than 37, stop the division. The reminder is 0. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}