Evaluate
\frac{20}{9}\approx 2.222222222
Factor
\frac{2 ^ {2} \cdot 5}{3 ^ {2}} = 2\frac{2}{9} = 2.2222222222222223
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\begin{array}{l}\phantom{72)}\phantom{1}\\72\overline{)160}\\\end{array}
Use the 1^{st} digit 1 from dividend 160
\begin{array}{l}\phantom{72)}0\phantom{2}\\72\overline{)160}\\\end{array}
Since 1 is less than 72, use the next digit 6 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{72)}0\phantom{3}\\72\overline{)160}\\\end{array}
Use the 2^{nd} digit 6 from dividend 160
\begin{array}{l}\phantom{72)}00\phantom{4}\\72\overline{)160}\\\end{array}
Since 16 is less than 72, use the next digit 0 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{72)}00\phantom{5}\\72\overline{)160}\\\end{array}
Use the 3^{rd} digit 0 from dividend 160
\begin{array}{l}\phantom{72)}002\phantom{6}\\72\overline{)160}\\\phantom{72)}\underline{\phantom{}144\phantom{}}\\\phantom{72)9}16\\\end{array}
Find closest multiple of 72 to 160. We see that 2 \times 72 = 144 is the nearest. Now subtract 144 from 160 to get reminder 16. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }16
Since 16 is less than 72, stop the division. The reminder is 16. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}