Evaluate
\frac{30}{17}\approx 1.764705882
Factor
\frac{2 \cdot 3 \cdot 5}{17} = 1\frac{13}{17} = 1.7647058823529411
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)150}\\\end{array}
Use the 1^{st} digit 1 from dividend 150
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)150}\\\end{array}
Since 1 is less than 85, use the next digit 5 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)150}\\\end{array}
Use the 2^{nd} digit 5 from dividend 150
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)150}\\\end{array}
Since 15 is less than 85, use the next digit 0 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)150}\\\end{array}
Use the 3^{rd} digit 0 from dividend 150
\begin{array}{l}\phantom{85)}001\phantom{6}\\85\overline{)150}\\\phantom{85)}\underline{\phantom{9}85\phantom{}}\\\phantom{85)9}65\\\end{array}
Find closest multiple of 85 to 150. We see that 1 \times 85 = 85 is the nearest. Now subtract 85 from 150 to get reminder 65. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }65
Since 65 is less than 85, stop the division. The reminder is 65. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}