Evaluate
\frac{56}{9}\approx 6.222222222
Factor
\frac{2 ^ {3} \cdot 7}{3 ^ {2}} = 6\frac{2}{9} = 6.222222222222222
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)112}\\\end{array}
Use the 1^{st} digit 1 from dividend 112
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)112}\\\end{array}
Since 1 is less than 18, use the next digit 1 from dividend 112 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)112}\\\end{array}
Use the 2^{nd} digit 1 from dividend 112
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)112}\\\end{array}
Since 11 is less than 18, use the next digit 2 from dividend 112 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)112}\\\end{array}
Use the 3^{rd} digit 2 from dividend 112
\begin{array}{l}\phantom{18)}006\phantom{6}\\18\overline{)112}\\\phantom{18)}\underline{\phantom{}108\phantom{}}\\\phantom{18)99}4\\\end{array}
Find closest multiple of 18 to 112. We see that 6 \times 18 = 108 is the nearest. Now subtract 108 from 112 to get reminder 4. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }4
Since 4 is less than 18, stop the division. The reminder is 4. 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}