Evaluate
\frac{34}{27}\approx 1.259259259
Factor
\frac{2 \cdot 17}{3 ^ {3}} = 1\frac{7}{27} = 1.2592592592592593
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)68}\\\end{array}
Use the 1^{st} digit 6 from dividend 68
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)68}\\\end{array}
Since 6 is less than 54, use the next digit 8 from dividend 68 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)68}\\\end{array}
Use the 2^{nd} digit 8 from dividend 68
\begin{array}{l}\phantom{54)}01\phantom{4}\\54\overline{)68}\\\phantom{54)}\underline{\phantom{}54\phantom{}}\\\phantom{54)}14\\\end{array}
Find closest multiple of 54 to 68. We see that 1 \times 54 = 54 is the nearest. Now subtract 54 from 68 to get reminder 14. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }14
Since 14 is less than 54, stop the division. The reminder is 14. 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}