Evaluate
\frac{78}{29}\approx 2.689655172
Factor
\frac{2 \cdot 3 \cdot 13}{29} = 2\frac{20}{29} = 2.689655172413793
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\begin{array}{l}\phantom{29)}\phantom{1}\\29\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{29)}0\phantom{2}\\29\overline{)78}\\\end{array}
Since 7 is less than 29, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{29)}0\phantom{3}\\29\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{29)}02\phantom{4}\\29\overline{)78}\\\phantom{29)}\underline{\phantom{}58\phantom{}}\\\phantom{29)}20\\\end{array}
Find closest multiple of 29 to 78. We see that 2 \times 29 = 58 is the nearest. Now subtract 58 from 78 to get reminder 20. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }20
Since 20 is less than 29, stop the division. The reminder is 20. The topmost line 02 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}