Evaluate
\frac{55}{12}\approx 4.583333333
Factor
\frac{5 \cdot 11}{2 ^ {2} \cdot 3} = 4\frac{7}{12} = 4.583333333333333
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)275}\\\end{array}
Use the 1^{st} digit 2 from dividend 275
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)275}\\\end{array}
Since 2 is less than 60, use the next digit 7 from dividend 275 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)275}\\\end{array}
Use the 2^{nd} digit 7 from dividend 275
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)275}\\\end{array}
Since 27 is less than 60, use the next digit 5 from dividend 275 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)275}\\\end{array}
Use the 3^{rd} digit 5 from dividend 275
\begin{array}{l}\phantom{60)}004\phantom{6}\\60\overline{)275}\\\phantom{60)}\underline{\phantom{}240\phantom{}}\\\phantom{60)9}35\\\end{array}
Find closest multiple of 60 to 275. We see that 4 \times 60 = 240 is the nearest. Now subtract 240 from 275 to get reminder 35. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }35
Since 35 is less than 60, stop the division. The reminder is 35. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}