Evaluate
\frac{39}{10}=3.9
Factor
\frac{3 \cdot 13}{2 \cdot 5} = 3\frac{9}{10} = 3.9
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)78}\\\end{array}
Since 7 is less than 20, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{20)}03\phantom{4}\\20\overline{)78}\\\phantom{20)}\underline{\phantom{}60\phantom{}}\\\phantom{20)}18\\\end{array}
Find closest multiple of 20 to 78. We see that 3 \times 20 = 60 is the nearest. Now subtract 60 from 78 to get reminder 18. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }18
Since 18 is less than 20, stop the division. The reminder is 18. 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}