Evaluate
\frac{38}{15}\approx 2.533333333
Factor
\frac{2 \cdot 19}{3 \cdot 5} = 2\frac{8}{15} = 2.533333333333333
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\begin{array}{l}\phantom{150)}\phantom{1}\\150\overline{)380}\\\end{array}
Use the 1^{st} digit 3 from dividend 380
\begin{array}{l}\phantom{150)}0\phantom{2}\\150\overline{)380}\\\end{array}
Since 3 is less than 150, use the next digit 8 from dividend 380 and add 0 to the quotient
\begin{array}{l}\phantom{150)}0\phantom{3}\\150\overline{)380}\\\end{array}
Use the 2^{nd} digit 8 from dividend 380
\begin{array}{l}\phantom{150)}00\phantom{4}\\150\overline{)380}\\\end{array}
Since 38 is less than 150, use the next digit 0 from dividend 380 and add 0 to the quotient
\begin{array}{l}\phantom{150)}00\phantom{5}\\150\overline{)380}\\\end{array}
Use the 3^{rd} digit 0 from dividend 380
\begin{array}{l}\phantom{150)}002\phantom{6}\\150\overline{)380}\\\phantom{150)}\underline{\phantom{}300\phantom{}}\\\phantom{150)9}80\\\end{array}
Find closest multiple of 150 to 380. We see that 2 \times 150 = 300 is the nearest. Now subtract 300 from 380 to get reminder 80. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }80
Since 80 is less than 150, stop the division. The reminder is 80. 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}