Evaluate
\frac{133}{36}\approx 3.694444444
Factor
\frac{7 \cdot 19}{2 ^ {2} \cdot 3 ^ {2}} = 3\frac{25}{36} = 3.6944444444444446
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)133}\\\end{array}
Use the 1^{st} digit 1 from dividend 133
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)133}\\\end{array}
Since 1 is less than 36, use the next digit 3 from dividend 133 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)133}\\\end{array}
Use the 2^{nd} digit 3 from dividend 133
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)133}\\\end{array}
Since 13 is less than 36, use the next digit 3 from dividend 133 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)133}\\\end{array}
Use the 3^{rd} digit 3 from dividend 133
\begin{array}{l}\phantom{36)}003\phantom{6}\\36\overline{)133}\\\phantom{36)}\underline{\phantom{}108\phantom{}}\\\phantom{36)9}25\\\end{array}
Find closest multiple of 36 to 133. We see that 3 \times 36 = 108 is the nearest. Now subtract 108 from 133 to get reminder 25. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }25
Since 25 is less than 36, stop the division. The reminder is 25. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}