Evaluate
\frac{113}{18}\approx 6.277777778
Factor
\frac{113}{2 \cdot 3 ^ {2}} = 6\frac{5}{18} = 6.277777777777778
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\begin{array}{l}\phantom{72)}\phantom{1}\\72\overline{)452}\\\end{array}
Use the 1^{st} digit 4 from dividend 452
\begin{array}{l}\phantom{72)}0\phantom{2}\\72\overline{)452}\\\end{array}
Since 4 is less than 72, use the next digit 5 from dividend 452 and add 0 to the quotient
\begin{array}{l}\phantom{72)}0\phantom{3}\\72\overline{)452}\\\end{array}
Use the 2^{nd} digit 5 from dividend 452
\begin{array}{l}\phantom{72)}00\phantom{4}\\72\overline{)452}\\\end{array}
Since 45 is less than 72, use the next digit 2 from dividend 452 and add 0 to the quotient
\begin{array}{l}\phantom{72)}00\phantom{5}\\72\overline{)452}\\\end{array}
Use the 3^{rd} digit 2 from dividend 452
\begin{array}{l}\phantom{72)}006\phantom{6}\\72\overline{)452}\\\phantom{72)}\underline{\phantom{}432\phantom{}}\\\phantom{72)9}20\\\end{array}
Find closest multiple of 72 to 452. We see that 6 \times 72 = 432 is the nearest. Now subtract 432 from 452 to get reminder 20. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }20
Since 20 is less than 72, stop the division. The reminder is 20. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}