Evaluate
\frac{86}{9}\approx 9.555555556
Factor
\frac{2 \cdot 43}{3 ^ {2}} = 9\frac{5}{9} = 9.555555555555555
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\begin{array}{l}\phantom{81)}\phantom{1}\\81\overline{)774}\\\end{array}
Use the 1^{st} digit 7 from dividend 774
\begin{array}{l}\phantom{81)}0\phantom{2}\\81\overline{)774}\\\end{array}
Since 7 is less than 81, use the next digit 7 from dividend 774 and add 0 to the quotient
\begin{array}{l}\phantom{81)}0\phantom{3}\\81\overline{)774}\\\end{array}
Use the 2^{nd} digit 7 from dividend 774
\begin{array}{l}\phantom{81)}00\phantom{4}\\81\overline{)774}\\\end{array}
Since 77 is less than 81, use the next digit 4 from dividend 774 and add 0 to the quotient
\begin{array}{l}\phantom{81)}00\phantom{5}\\81\overline{)774}\\\end{array}
Use the 3^{rd} digit 4 from dividend 774
\begin{array}{l}\phantom{81)}009\phantom{6}\\81\overline{)774}\\\phantom{81)}\underline{\phantom{}729\phantom{}}\\\phantom{81)9}45\\\end{array}
Find closest multiple of 81 to 774. We see that 9 \times 81 = 729 is the nearest. Now subtract 729 from 774 to get reminder 45. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }45
Since 45 is less than 81, stop the division. The reminder is 45. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}