Evaluate
\frac{127}{30}\approx 4.233333333
Factor
\frac{127}{2 \cdot 3 \cdot 5} = 4\frac{7}{30} = 4.233333333333333
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)254}\\\end{array}
Use the 1^{st} digit 2 from dividend 254
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)254}\\\end{array}
Since 2 is less than 60, use the next digit 5 from dividend 254 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)254}\\\end{array}
Use the 2^{nd} digit 5 from dividend 254
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)254}\\\end{array}
Since 25 is less than 60, use the next digit 4 from dividend 254 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)254}\\\end{array}
Use the 3^{rd} digit 4 from dividend 254
\begin{array}{l}\phantom{60)}004\phantom{6}\\60\overline{)254}\\\phantom{60)}\underline{\phantom{}240\phantom{}}\\\phantom{60)9}14\\\end{array}
Find closest multiple of 60 to 254. We see that 4 \times 60 = 240 is the nearest. Now subtract 240 from 254 to get reminder 14. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }14
Since 14 is less than 60, stop the division. The reminder is 14. 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}