Evaluate
\frac{450}{37}\approx 12.162162162
Factor
\frac{2 \cdot 3 ^ {2} \cdot 5 ^ {2}}{37} = 12\frac{6}{37} = 12.162162162162161
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\begin{array}{l}\phantom{37)}\phantom{1}\\37\overline{)450}\\\end{array}
Use the 1^{st} digit 4 from dividend 450
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)450}\\\end{array}
Since 4 is less than 37, use the next digit 5 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)450}\\\end{array}
Use the 2^{nd} digit 5 from dividend 450
\begin{array}{l}\phantom{37)}01\phantom{4}\\37\overline{)450}\\\phantom{37)}\underline{\phantom{}37\phantom{9}}\\\phantom{37)9}8\\\end{array}
Find closest multiple of 37 to 45. We see that 1 \times 37 = 37 is the nearest. Now subtract 37 from 45 to get reminder 8. Add 1 to quotient.
\begin{array}{l}\phantom{37)}01\phantom{5}\\37\overline{)450}\\\phantom{37)}\underline{\phantom{}37\phantom{9}}\\\phantom{37)9}80\\\end{array}
Use the 3^{rd} digit 0 from dividend 450
\begin{array}{l}\phantom{37)}012\phantom{6}\\37\overline{)450}\\\phantom{37)}\underline{\phantom{}37\phantom{9}}\\\phantom{37)9}80\\\phantom{37)}\underline{\phantom{9}74\phantom{}}\\\phantom{37)99}6\\\end{array}
Find closest multiple of 37 to 80. We see that 2 \times 37 = 74 is the nearest. Now subtract 74 from 80 to get reminder 6. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }6
Since 6 is less than 37, stop the division. The reminder is 6. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}