Evaluate
\frac{51}{11}\approx 4.636363636
Factor
\frac{3 \cdot 17}{11} = 4\frac{7}{11} = 4.636363636363637
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)51}\\\end{array}
Use the 1^{st} digit 5 from dividend 51
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)51}\\\end{array}
Since 5 is less than 11, use the next digit 1 from dividend 51 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)51}\\\end{array}
Use the 2^{nd} digit 1 from dividend 51
\begin{array}{l}\phantom{11)}04\phantom{4}\\11\overline{)51}\\\phantom{11)}\underline{\phantom{}44\phantom{}}\\\phantom{11)9}7\\\end{array}
Find closest multiple of 11 to 51. We see that 4 \times 11 = 44 is the nearest. Now subtract 44 from 51 to get reminder 7. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }7
Since 7 is less than 11, stop the division. The reminder is 7. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}