Evaluate
\frac{39}{28}\approx 1.392857143
Factor
\frac{3 \cdot 13}{2 ^ {2} \cdot 7} = 1\frac{11}{28} = 1.3928571428571428
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\begin{array}{l}\phantom{56)}\phantom{1}\\56\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{56)}0\phantom{2}\\56\overline{)78}\\\end{array}
Since 7 is less than 56, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{56)}0\phantom{3}\\56\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{56)}01\phantom{4}\\56\overline{)78}\\\phantom{56)}\underline{\phantom{}56\phantom{}}\\\phantom{56)}22\\\end{array}
Find closest multiple of 56 to 78. We see that 1 \times 56 = 56 is the nearest. Now subtract 56 from 78 to get reminder 22. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }22
Since 22 is less than 56, stop the division. The reminder is 22. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}