Evaluate
\frac{40}{9}\approx 4.444444444
Factor
\frac{2 ^ {3} \cdot 5}{3 ^ {2}} = 4\frac{4}{9} = 4.444444444444445
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)160}\\\end{array}
Use the 1^{st} digit 1 from dividend 160
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)160}\\\end{array}
Since 1 is less than 36, use the next digit 6 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)160}\\\end{array}
Use the 2^{nd} digit 6 from dividend 160
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)160}\\\end{array}
Since 16 is less than 36, use the next digit 0 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)160}\\\end{array}
Use the 3^{rd} digit 0 from dividend 160
\begin{array}{l}\phantom{36)}004\phantom{6}\\36\overline{)160}\\\phantom{36)}\underline{\phantom{}144\phantom{}}\\\phantom{36)9}16\\\end{array}
Find closest multiple of 36 to 160. We see that 4 \times 36 = 144 is the nearest. Now subtract 144 from 160 to get reminder 16. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }16
Since 16 is less than 36, stop the division. The reminder is 16. The topmost line 004 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}