Evaluate
\frac{32}{15}\approx 2.133333333
Factor
\frac{2 ^ {5}}{3 \cdot 5} = 2\frac{2}{15} \approx 2.133333333
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)96}\\\end{array}
Use the 1^{st} digit 9 from dividend 96
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)96}\\\end{array}
Since 9 is less than 45, use the next digit 6 from dividend 96 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)96}\\\end{array}
Use the 2^{nd} digit 6 from dividend 96
\begin{array}{l}\phantom{45)}02\phantom{4}\\45\overline{)96}\\\phantom{45)}\underline{\phantom{}90\phantom{}}\\\phantom{45)9}6\\\end{array}
Find closest multiple of 45 to 96. We see that 2 \times 45 = 90 is the nearest. Now subtract 90 from 96 to get reminder 6. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }6
Since 6 is less than 45, stop the division. The reminder is 6. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}