Evaluate
\frac{775}{12}\approx 64.583333333
Factor
\frac{5 ^ {2} \cdot 31}{2 ^ {2} \cdot 3} = 64\frac{7}{12} = 64.58333333333333
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)775}\\\end{array}
Use the 1^{st} digit 7 from dividend 775
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)775}\\\end{array}
Since 7 is less than 12, use the next digit 7 from dividend 775 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)775}\\\end{array}
Use the 2^{nd} digit 7 from dividend 775
\begin{array}{l}\phantom{12)}06\phantom{4}\\12\overline{)775}\\\phantom{12)}\underline{\phantom{}72\phantom{9}}\\\phantom{12)9}5\\\end{array}
Find closest multiple of 12 to 77. We see that 6 \times 12 = 72 is the nearest. Now subtract 72 from 77 to get reminder 5. Add 6 to quotient.
\begin{array}{l}\phantom{12)}06\phantom{5}\\12\overline{)775}\\\phantom{12)}\underline{\phantom{}72\phantom{9}}\\\phantom{12)9}55\\\end{array}
Use the 3^{rd} digit 5 from dividend 775
\begin{array}{l}\phantom{12)}064\phantom{6}\\12\overline{)775}\\\phantom{12)}\underline{\phantom{}72\phantom{9}}\\\phantom{12)9}55\\\phantom{12)}\underline{\phantom{9}48\phantom{}}\\\phantom{12)99}7\\\end{array}
Find closest multiple of 12 to 55. We see that 4 \times 12 = 48 is the nearest. Now subtract 48 from 55 to get reminder 7. Add 4 to quotient.
\text{Quotient: }64 \text{Reminder: }7
Since 7 is less than 12, stop the division. The reminder is 7. The topmost line 064 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 64.
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}