Evaluate
\frac{254}{63}\approx 4.031746032
Factor
\frac{2 \cdot 127}{3 ^ {2} \cdot 7} = 4\frac{2}{63} = 4.031746031746032
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)254}\\\end{array}
Use the 1^{st} digit 2 from dividend 254
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)254}\\\end{array}
Since 2 is less than 63, use the next digit 5 from dividend 254 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)254}\\\end{array}
Use the 2^{nd} digit 5 from dividend 254
\begin{array}{l}\phantom{63)}00\phantom{4}\\63\overline{)254}\\\end{array}
Since 25 is less than 63, use the next digit 4 from dividend 254 and add 0 to the quotient
\begin{array}{l}\phantom{63)}00\phantom{5}\\63\overline{)254}\\\end{array}
Use the 3^{rd} digit 4 from dividend 254
\begin{array}{l}\phantom{63)}004\phantom{6}\\63\overline{)254}\\\phantom{63)}\underline{\phantom{}252\phantom{}}\\\phantom{63)99}2\\\end{array}
Find closest multiple of 63 to 254. We see that 4 \times 63 = 252 is the nearest. Now subtract 252 from 254 to get reminder 2. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }2
Since 2 is less than 63, stop the division. The reminder is 2. 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}