Evaluate
\frac{227}{45}\approx 5.044444444
Factor
\frac{227}{3 ^ {2} \cdot 5} = 5\frac{2}{45} = 5.044444444444444
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)227}\\\end{array}
Use the 1^{st} digit 2 from dividend 227
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)227}\\\end{array}
Since 2 is less than 45, use the next digit 2 from dividend 227 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)227}\\\end{array}
Use the 2^{nd} digit 2 from dividend 227
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)227}\\\end{array}
Since 22 is less than 45, use the next digit 7 from dividend 227 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)227}\\\end{array}
Use the 3^{rd} digit 7 from dividend 227
\begin{array}{l}\phantom{45)}005\phantom{6}\\45\overline{)227}\\\phantom{45)}\underline{\phantom{}225\phantom{}}\\\phantom{45)99}2\\\end{array}
Find closest multiple of 45 to 227. We see that 5 \times 45 = 225 is the nearest. Now subtract 225 from 227 to get reminder 2. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }2
Since 2 is less than 45, stop the division. The reminder is 2. 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}