Evaluate
\frac{17}{5}=3.4
Factor
\frac{17}{5} = 3\frac{2}{5} = 3.4
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)221}\\\end{array}
Use the 1^{st} digit 2 from dividend 221
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)221}\\\end{array}
Since 2 is less than 65, use the next digit 2 from dividend 221 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)221}\\\end{array}
Use the 2^{nd} digit 2 from dividend 221
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)221}\\\end{array}
Since 22 is less than 65, use the next digit 1 from dividend 221 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)221}\\\end{array}
Use the 3^{rd} digit 1 from dividend 221
\begin{array}{l}\phantom{65)}003\phantom{6}\\65\overline{)221}\\\phantom{65)}\underline{\phantom{}195\phantom{}}\\\phantom{65)9}26\\\end{array}
Find closest multiple of 65 to 221. We see that 3 \times 65 = 195 is the nearest. Now subtract 195 from 221 to get reminder 26. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }26
Since 26 is less than 65, stop the division. The reminder is 26. 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}