Evaluate
\frac{55}{17}\approx 3.235294118
Factor
\frac{5 \cdot 11}{17} = 3\frac{4}{17} = 3.235294117647059
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)275}\\\end{array}
Use the 1^{st} digit 2 from dividend 275
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)275}\\\end{array}
Since 2 is less than 85, use the next digit 7 from dividend 275 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)275}\\\end{array}
Use the 2^{nd} digit 7 from dividend 275
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)275}\\\end{array}
Since 27 is less than 85, use the next digit 5 from dividend 275 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)275}\\\end{array}
Use the 3^{rd} digit 5 from dividend 275
\begin{array}{l}\phantom{85)}003\phantom{6}\\85\overline{)275}\\\phantom{85)}\underline{\phantom{}255\phantom{}}\\\phantom{85)9}20\\\end{array}
Find closest multiple of 85 to 275. We see that 3 \times 85 = 255 is the nearest. Now subtract 255 from 275 to get reminder 20. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }20
Since 20 is less than 85, stop the division. The reminder is 20. 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}