Evaluate
\frac{112}{9}\approx 12.444444444
Factor
\frac{2 ^ {4} \cdot 7}{3 ^ {2}} = 12\frac{4}{9} = 12.444444444444445
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)224}\\\end{array}
Use the 1^{st} digit 2 from dividend 224
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)224}\\\end{array}
Since 2 is less than 18, use the next digit 2 from dividend 224 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)224}\\\end{array}
Use the 2^{nd} digit 2 from dividend 224
\begin{array}{l}\phantom{18)}01\phantom{4}\\18\overline{)224}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}4\\\end{array}
Find closest multiple of 18 to 22. We see that 1 \times 18 = 18 is the nearest. Now subtract 18 from 22 to get reminder 4. Add 1 to quotient.
\begin{array}{l}\phantom{18)}01\phantom{5}\\18\overline{)224}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}44\\\end{array}
Use the 3^{rd} digit 4 from dividend 224
\begin{array}{l}\phantom{18)}012\phantom{6}\\18\overline{)224}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}44\\\phantom{18)}\underline{\phantom{9}36\phantom{}}\\\phantom{18)99}8\\\end{array}
Find closest multiple of 18 to 44. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 44 to get reminder 8. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }8
Since 8 is less than 18, stop the division. The reminder is 8. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}