Evaluate
\frac{131}{24}\approx 5.458333333
Factor
\frac{131}{2 ^ {3} \cdot 3} = 5\frac{11}{24} = 5.458333333333333
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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)655}\\\end{array}
Use the 1^{st} digit 6 from dividend 655
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)655}\\\end{array}
Since 6 is less than 120, use the next digit 5 from dividend 655 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)655}\\\end{array}
Use the 2^{nd} digit 5 from dividend 655
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)655}\\\end{array}
Since 65 is less than 120, use the next digit 5 from dividend 655 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)655}\\\end{array}
Use the 3^{rd} digit 5 from dividend 655
\begin{array}{l}\phantom{120)}005\phantom{6}\\120\overline{)655}\\\phantom{120)}\underline{\phantom{}600\phantom{}}\\\phantom{120)9}55\\\end{array}
Find closest multiple of 120 to 655. We see that 5 \times 120 = 600 is the nearest. Now subtract 600 from 655 to get reminder 55. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }55
Since 55 is less than 120, stop the division. The reminder is 55. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}