Evaluate
\frac{23}{4}=5.75
Factor
\frac{23}{2 ^ {2}} = 5\frac{3}{4} = 5.75
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)575}\\\end{array}
Use the 1^{st} digit 5 from dividend 575
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)575}\\\end{array}
Since 5 is less than 100, use the next digit 7 from dividend 575 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)575}\\\end{array}
Use the 2^{nd} digit 7 from dividend 575
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)575}\\\end{array}
Since 57 is less than 100, use the next digit 5 from dividend 575 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)575}\\\end{array}
Use the 3^{rd} digit 5 from dividend 575
\begin{array}{l}\phantom{100)}005\phantom{6}\\100\overline{)575}\\\phantom{100)}\underline{\phantom{}500\phantom{}}\\\phantom{100)9}75\\\end{array}
Find closest multiple of 100 to 575. We see that 5 \times 100 = 500 is the nearest. Now subtract 500 from 575 to get reminder 75. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }75
Since 75 is less than 100, stop the division. The reminder is 75. 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}