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{72)}\phantom{1}\\72\overline{)320}\\\end{array}
Use the 1^{st} digit 3 from dividend 320
\begin{array}{l}\phantom{72)}0\phantom{2}\\72\overline{)320}\\\end{array}
Since 3 is less than 72, use the next digit 2 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{72)}0\phantom{3}\\72\overline{)320}\\\end{array}
Use the 2^{nd} digit 2 from dividend 320
\begin{array}{l}\phantom{72)}00\phantom{4}\\72\overline{)320}\\\end{array}
Since 32 is less than 72, use the next digit 0 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{72)}00\phantom{5}\\72\overline{)320}\\\end{array}
Use the 3^{rd} digit 0 from dividend 320
\begin{array}{l}\phantom{72)}004\phantom{6}\\72\overline{)320}\\\phantom{72)}\underline{\phantom{}288\phantom{}}\\\phantom{72)9}32\\\end{array}
Find closest multiple of 72 to 320. We see that 4 \times 72 = 288 is the nearest. Now subtract 288 from 320 to get reminder 32. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }32
Since 32 is less than 72, stop the division. The reminder is 32. 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}