Evaluate
\frac{227}{30}\approx 7.566666667
Factor
\frac{227}{2 \cdot 3 \cdot 5} = 7\frac{17}{30} = 7.566666666666666
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)681}\\\end{array}
Use the 1^{st} digit 6 from dividend 681
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)681}\\\end{array}
Since 6 is less than 90, use the next digit 8 from dividend 681 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)681}\\\end{array}
Use the 2^{nd} digit 8 from dividend 681
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)681}\\\end{array}
Since 68 is less than 90, use the next digit 1 from dividend 681 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)681}\\\end{array}
Use the 3^{rd} digit 1 from dividend 681
\begin{array}{l}\phantom{90)}007\phantom{6}\\90\overline{)681}\\\phantom{90)}\underline{\phantom{}630\phantom{}}\\\phantom{90)9}51\\\end{array}
Find closest multiple of 90 to 681. We see that 7 \times 90 = 630 is the nearest. Now subtract 630 from 681 to get reminder 51. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }51
Since 51 is less than 90, stop the division. The reminder is 51. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}