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{60)}\phantom{1}\\60\overline{)340}\\\end{array}
Use the 1^{st} digit 3 from dividend 340
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)340}\\\end{array}
Since 3 is less than 60, use the next digit 4 from dividend 340 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)340}\\\end{array}
Use the 2^{nd} digit 4 from dividend 340
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)340}\\\end{array}
Since 34 is less than 60, use the next digit 0 from dividend 340 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)340}\\\end{array}
Use the 3^{rd} digit 0 from dividend 340
\begin{array}{l}\phantom{60)}005\phantom{6}\\60\overline{)340}\\\phantom{60)}\underline{\phantom{}300\phantom{}}\\\phantom{60)9}40\\\end{array}
Find closest multiple of 60 to 340. We see that 5 \times 60 = 300 is the nearest. Now subtract 300 from 340 to get reminder 40. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }40
Since 40 is less than 60, stop the division. The reminder is 40. The topmost line 005 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}