Evaluate
\frac{80}{9}\approx 8.888888889
Factor
\frac{2 ^ {4} \cdot 5}{3 ^ {2}} = 8\frac{8}{9} = 8.88888888888889
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)400}\\\end{array}
Use the 1^{st} digit 4 from dividend 400
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)400}\\\end{array}
Since 4 is less than 45, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 400
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)400}\\\end{array}
Since 40 is less than 45, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)400}\\\end{array}
Use the 3^{rd} digit 0 from dividend 400
\begin{array}{l}\phantom{45)}008\phantom{6}\\45\overline{)400}\\\phantom{45)}\underline{\phantom{}360\phantom{}}\\\phantom{45)9}40\\\end{array}
Find closest multiple of 45 to 400. We see that 8 \times 45 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }40
Since 40 is less than 45, stop the division. The reminder is 40. 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}