Evaluate
\frac{198}{43}\approx 4.604651163
Factor
\frac{2 \cdot 3 ^ {2} \cdot 11}{43} = 4\frac{26}{43} = 4.604651162790698
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\begin{array}{l}\phantom{172)}\phantom{1}\\172\overline{)792}\\\end{array}
Use the 1^{st} digit 7 from dividend 792
\begin{array}{l}\phantom{172)}0\phantom{2}\\172\overline{)792}\\\end{array}
Since 7 is less than 172, use the next digit 9 from dividend 792 and add 0 to the quotient
\begin{array}{l}\phantom{172)}0\phantom{3}\\172\overline{)792}\\\end{array}
Use the 2^{nd} digit 9 from dividend 792
\begin{array}{l}\phantom{172)}00\phantom{4}\\172\overline{)792}\\\end{array}
Since 79 is less than 172, use the next digit 2 from dividend 792 and add 0 to the quotient
\begin{array}{l}\phantom{172)}00\phantom{5}\\172\overline{)792}\\\end{array}
Use the 3^{rd} digit 2 from dividend 792
\begin{array}{l}\phantom{172)}004\phantom{6}\\172\overline{)792}\\\phantom{172)}\underline{\phantom{}688\phantom{}}\\\phantom{172)}104\\\end{array}
Find closest multiple of 172 to 792. We see that 4 \times 172 = 688 is the nearest. Now subtract 688 from 792 to get reminder 104. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }104
Since 104 is less than 172, stop the division. The reminder is 104. 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}