Evaluate
\frac{90}{23}\approx 3.913043478
Factor
\frac{2 \cdot 3 ^ {2} \cdot 5}{23} = 3\frac{21}{23} = 3.9130434782608696
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)90}\\\end{array}
Use the 1^{st} digit 9 from dividend 90
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)90}\\\end{array}
Since 9 is less than 23, use the next digit 0 from dividend 90 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)90}\\\end{array}
Use the 2^{nd} digit 0 from dividend 90
\begin{array}{l}\phantom{23)}03\phantom{4}\\23\overline{)90}\\\phantom{23)}\underline{\phantom{}69\phantom{}}\\\phantom{23)}21\\\end{array}
Find closest multiple of 23 to 90. We see that 3 \times 23 = 69 is the nearest. Now subtract 69 from 90 to get reminder 21. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }21
Since 21 is less than 23, stop the division. The reminder is 21. The topmost line 03 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}