Evaluate
\frac{98}{27}\approx 3.62962963
Factor
\frac{2 \cdot 7 ^ {2}}{3 ^ {3}} = 3\frac{17}{27} = 3.6296296296296298
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)196}\\\end{array}
Use the 1^{st} digit 1 from dividend 196
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)196}\\\end{array}
Since 1 is less than 54, use the next digit 9 from dividend 196 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)196}\\\end{array}
Use the 2^{nd} digit 9 from dividend 196
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)196}\\\end{array}
Since 19 is less than 54, use the next digit 6 from dividend 196 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)196}\\\end{array}
Use the 3^{rd} digit 6 from dividend 196
\begin{array}{l}\phantom{54)}003\phantom{6}\\54\overline{)196}\\\phantom{54)}\underline{\phantom{}162\phantom{}}\\\phantom{54)9}34\\\end{array}
Find closest multiple of 54 to 196. We see that 3 \times 54 = 162 is the nearest. Now subtract 162 from 196 to get reminder 34. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }34
Since 34 is less than 54, stop the division. The reminder is 34. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}