Evaluate
\frac{178}{9}\approx 19.777777778
Factor
\frac{2 \cdot 89}{3 ^ {2}} = 19\frac{7}{9} = 19.77777777777778
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)356}\\\end{array}
Use the 1^{st} digit 3 from dividend 356
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)356}\\\end{array}
Since 3 is less than 18, use the next digit 5 from dividend 356 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)356}\\\end{array}
Use the 2^{nd} digit 5 from dividend 356
\begin{array}{l}\phantom{18)}01\phantom{4}\\18\overline{)356}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)}17\\\end{array}
Find closest multiple of 18 to 35. We see that 1 \times 18 = 18 is the nearest. Now subtract 18 from 35 to get reminder 17. Add 1 to quotient.
\begin{array}{l}\phantom{18)}01\phantom{5}\\18\overline{)356}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)}176\\\end{array}
Use the 3^{rd} digit 6 from dividend 356
\begin{array}{l}\phantom{18)}019\phantom{6}\\18\overline{)356}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)}176\\\phantom{18)}\underline{\phantom{}162\phantom{}}\\\phantom{18)9}14\\\end{array}
Find closest multiple of 18 to 176. We see that 9 \times 18 = 162 is the nearest. Now subtract 162 from 176 to get reminder 14. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }14
Since 14 is less than 18, stop the division. The reminder is 14. The topmost line 019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.
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}