Evaluate
\frac{28}{27}\approx 1.037037037
Factor
\frac{2 ^ {2} \cdot 7}{3 ^ {3}} = 1\frac{1}{27} = 1.037037037037037
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)56}\\\end{array}
Use the 1^{st} digit 5 from dividend 56
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)56}\\\end{array}
Since 5 is less than 54, use the next digit 6 from dividend 56 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)56}\\\end{array}
Use the 2^{nd} digit 6 from dividend 56
\begin{array}{l}\phantom{54)}01\phantom{4}\\54\overline{)56}\\\phantom{54)}\underline{\phantom{}54\phantom{}}\\\phantom{54)9}2\\\end{array}
Find closest multiple of 54 to 56. We see that 1 \times 54 = 54 is the nearest. Now subtract 54 from 56 to get reminder 2. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }2
Since 2 is less than 54, stop the division. The reminder is 2. 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}