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{300)}\phantom{1}\\300\overline{)760}\\\end{array}
Use the 1^{st} digit 7 from dividend 760
\begin{array}{l}\phantom{300)}0\phantom{2}\\300\overline{)760}\\\end{array}
Since 7 is less than 300, use the next digit 6 from dividend 760 and add 0 to the quotient
\begin{array}{l}\phantom{300)}0\phantom{3}\\300\overline{)760}\\\end{array}
Use the 2^{nd} digit 6 from dividend 760
\begin{array}{l}\phantom{300)}00\phantom{4}\\300\overline{)760}\\\end{array}
Since 76 is less than 300, use the next digit 0 from dividend 760 and add 0 to the quotient
\begin{array}{l}\phantom{300)}00\phantom{5}\\300\overline{)760}\\\end{array}
Use the 3^{rd} digit 0 from dividend 760
\begin{array}{l}\phantom{300)}002\phantom{6}\\300\overline{)760}\\\phantom{300)}\underline{\phantom{}600\phantom{}}\\\phantom{300)}160\\\end{array}
Find closest multiple of 300 to 760. We see that 2 \times 300 = 600 is the nearest. Now subtract 600 from 760 to get reminder 160. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }160
Since 160 is less than 300, stop the division. The reminder is 160. 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}