Evaluate
\frac{5}{2}=2.5
Factor
\frac{5}{2} = 2\frac{1}{2} = 2.5
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\begin{array}{l}\phantom{46)}\phantom{1}\\46\overline{)115}\\\end{array}
Use the 1^{st} digit 1 from dividend 115
\begin{array}{l}\phantom{46)}0\phantom{2}\\46\overline{)115}\\\end{array}
Since 1 is less than 46, use the next digit 1 from dividend 115 and add 0 to the quotient
\begin{array}{l}\phantom{46)}0\phantom{3}\\46\overline{)115}\\\end{array}
Use the 2^{nd} digit 1 from dividend 115
\begin{array}{l}\phantom{46)}00\phantom{4}\\46\overline{)115}\\\end{array}
Since 11 is less than 46, use the next digit 5 from dividend 115 and add 0 to the quotient
\begin{array}{l}\phantom{46)}00\phantom{5}\\46\overline{)115}\\\end{array}
Use the 3^{rd} digit 5 from dividend 115
\begin{array}{l}\phantom{46)}002\phantom{6}\\46\overline{)115}\\\phantom{46)}\underline{\phantom{9}92\phantom{}}\\\phantom{46)9}23\\\end{array}
Find closest multiple of 46 to 115. We see that 2 \times 46 = 92 is the nearest. Now subtract 92 from 115 to get reminder 23. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }23
Since 23 is less than 46, stop the division. The reminder is 23. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}