Evaluate
\frac{468}{127}\approx 3.68503937
Factor
\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 13}{127} = 3\frac{87}{127} = 3.6850393700787403
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\begin{array}{l}\phantom{254)}\phantom{1}\\254\overline{)936}\\\end{array}
Use the 1^{st} digit 9 from dividend 936
\begin{array}{l}\phantom{254)}0\phantom{2}\\254\overline{)936}\\\end{array}
Since 9 is less than 254, use the next digit 3 from dividend 936 and add 0 to the quotient
\begin{array}{l}\phantom{254)}0\phantom{3}\\254\overline{)936}\\\end{array}
Use the 2^{nd} digit 3 from dividend 936
\begin{array}{l}\phantom{254)}00\phantom{4}\\254\overline{)936}\\\end{array}
Since 93 is less than 254, use the next digit 6 from dividend 936 and add 0 to the quotient
\begin{array}{l}\phantom{254)}00\phantom{5}\\254\overline{)936}\\\end{array}
Use the 3^{rd} digit 6 from dividend 936
\begin{array}{l}\phantom{254)}003\phantom{6}\\254\overline{)936}\\\phantom{254)}\underline{\phantom{}762\phantom{}}\\\phantom{254)}174\\\end{array}
Find closest multiple of 254 to 936. We see that 3 \times 254 = 762 is the nearest. Now subtract 762 from 936 to get reminder 174. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }174
Since 174 is less than 254, stop the division. The reminder is 174. 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}