Evaluate
\frac{30}{13}\approx 2.307692308
Factor
\frac{2 \cdot 3 \cdot 5}{13} = 2\frac{4}{13} = 2.3076923076923075
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)150}\\\end{array}
Use the 1^{st} digit 1 from dividend 150
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)150}\\\end{array}
Since 1 is less than 65, use the next digit 5 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)150}\\\end{array}
Use the 2^{nd} digit 5 from dividend 150
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)150}\\\end{array}
Since 15 is less than 65, use the next digit 0 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)150}\\\end{array}
Use the 3^{rd} digit 0 from dividend 150
\begin{array}{l}\phantom{65)}002\phantom{6}\\65\overline{)150}\\\phantom{65)}\underline{\phantom{}130\phantom{}}\\\phantom{65)9}20\\\end{array}
Find closest multiple of 65 to 150. We see that 2 \times 65 = 130 is the nearest. Now subtract 130 from 150 to get reminder 20. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }20
Since 20 is less than 65, stop the division. The reminder is 20. The topmost line 002 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}