Evaluate
\frac{185}{36}\approx 5.138888889
Factor
\frac{5 \cdot 37}{2 ^ {2} \cdot 3 ^ {2}} = 5\frac{5}{36} = 5.138888888888889
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)185}\\\end{array}
Use the 1^{st} digit 1 from dividend 185
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)185}\\\end{array}
Since 1 is less than 36, use the next digit 8 from dividend 185 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)185}\\\end{array}
Use the 2^{nd} digit 8 from dividend 185
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)185}\\\end{array}
Since 18 is less than 36, use the next digit 5 from dividend 185 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)185}\\\end{array}
Use the 3^{rd} digit 5 from dividend 185
\begin{array}{l}\phantom{36)}005\phantom{6}\\36\overline{)185}\\\phantom{36)}\underline{\phantom{}180\phantom{}}\\\phantom{36)99}5\\\end{array}
Find closest multiple of 36 to 185. We see that 5 \times 36 = 180 is the nearest. Now subtract 180 from 185 to get reminder 5. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }5
Since 5 is less than 36, stop the division. The reminder is 5. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}