Evaluate
\frac{17}{3}\approx 5.666666667
Factor
\frac{17}{3} = 5\frac{2}{3} = 5.666666666666667
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)85}\\\end{array}
Use the 1^{st} digit 8 from dividend 85
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)85}\\\end{array}
Since 8 is less than 15, use the next digit 5 from dividend 85 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)85}\\\end{array}
Use the 2^{nd} digit 5 from dividend 85
\begin{array}{l}\phantom{15)}05\phantom{4}\\15\overline{)85}\\\phantom{15)}\underline{\phantom{}75\phantom{}}\\\phantom{15)}10\\\end{array}
Find closest multiple of 15 to 85. We see that 5 \times 15 = 75 is the nearest. Now subtract 75 from 85 to get reminder 10. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }10
Since 10 is less than 15, stop the division. The reminder is 10. The topmost line 05 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}