Evaluate
\frac{391}{45}\approx 8.688888889
Factor
\frac{17 \cdot 23}{3 ^ {2} \cdot 5} = 8\frac{31}{45} = 8.688888888888888
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)391}\\\end{array}
Use the 1^{st} digit 3 from dividend 391
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)391}\\\end{array}
Since 3 is less than 45, use the next digit 9 from dividend 391 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)391}\\\end{array}
Use the 2^{nd} digit 9 from dividend 391
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)391}\\\end{array}
Since 39 is less than 45, use the next digit 1 from dividend 391 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)391}\\\end{array}
Use the 3^{rd} digit 1 from dividend 391
\begin{array}{l}\phantom{45)}008\phantom{6}\\45\overline{)391}\\\phantom{45)}\underline{\phantom{}360\phantom{}}\\\phantom{45)9}31\\\end{array}
Find closest multiple of 45 to 391. We see that 8 \times 45 = 360 is the nearest. Now subtract 360 from 391 to get reminder 31. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }31
Since 31 is less than 45, stop the division. The reminder is 31. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}