Evaluate
\frac{27}{7}\approx 3.857142857
Factor
\frac{3 ^ {3}}{7} = 3\frac{6}{7} = 3.857142857142857
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)135}\\\end{array}
Use the 1^{st} digit 1 from dividend 135
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)135}\\\end{array}
Since 1 is less than 35, use the next digit 3 from dividend 135 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)135}\\\end{array}
Use the 2^{nd} digit 3 from dividend 135
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)135}\\\end{array}
Since 13 is less than 35, use the next digit 5 from dividend 135 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)135}\\\end{array}
Use the 3^{rd} digit 5 from dividend 135
\begin{array}{l}\phantom{35)}003\phantom{6}\\35\overline{)135}\\\phantom{35)}\underline{\phantom{}105\phantom{}}\\\phantom{35)9}30\\\end{array}
Find closest multiple of 35 to 135. We see that 3 \times 35 = 105 is the nearest. Now subtract 105 from 135 to get reminder 30. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }30
Since 30 is less than 35, stop the division. The reminder is 30. The topmost line 003 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}