Evaluate
\frac{51}{14}\approx 3.642857143
Factor
\frac{3 \cdot 17}{2 \cdot 7} = 3\frac{9}{14} = 3.642857142857143
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)255}\\\end{array}
Use the 1^{st} digit 2 from dividend 255
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)255}\\\end{array}
Since 2 is less than 70, use the next digit 5 from dividend 255 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)255}\\\end{array}
Use the 2^{nd} digit 5 from dividend 255
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)255}\\\end{array}
Since 25 is less than 70, use the next digit 5 from dividend 255 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)255}\\\end{array}
Use the 3^{rd} digit 5 from dividend 255
\begin{array}{l}\phantom{70)}003\phantom{6}\\70\overline{)255}\\\phantom{70)}\underline{\phantom{}210\phantom{}}\\\phantom{70)9}45\\\end{array}
Find closest multiple of 70 to 255. We see that 3 \times 70 = 210 is the nearest. Now subtract 210 from 255 to get reminder 45. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }45
Since 45 is less than 70, stop the division. The reminder is 45. 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}