Evaluate
\frac{60}{17}\approx 3.529411765
Factor
\frac{2 ^ {2} \cdot 3 \cdot 5}{17} = 3\frac{9}{17} = 3.5294117647058822
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)300}\\\end{array}
Use the 1^{st} digit 3 from dividend 300
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)300}\\\end{array}
Since 3 is less than 85, use the next digit 0 from dividend 300 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)300}\\\end{array}
Use the 2^{nd} digit 0 from dividend 300
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)300}\\\end{array}
Since 30 is less than 85, use the next digit 0 from dividend 300 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)300}\\\end{array}
Use the 3^{rd} digit 0 from dividend 300
\begin{array}{l}\phantom{85)}003\phantom{6}\\85\overline{)300}\\\phantom{85)}\underline{\phantom{}255\phantom{}}\\\phantom{85)9}45\\\end{array}
Find closest multiple of 85 to 300. We see that 3 \times 85 = 255 is the nearest. Now subtract 255 from 300 to get reminder 45. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }45
Since 45 is less than 85, stop the division. The reminder is 45. 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}