Evaluate
\frac{9}{4}=2.25
Factor
\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)225}\\\end{array}
Use the 1^{st} digit 2 from dividend 225
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)225}\\\end{array}
Since 2 is less than 100, use the next digit 2 from dividend 225 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)225}\\\end{array}
Use the 2^{nd} digit 2 from dividend 225
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)225}\\\end{array}
Since 22 is less than 100, use the next digit 5 from dividend 225 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)225}\\\end{array}
Use the 3^{rd} digit 5 from dividend 225
\begin{array}{l}\phantom{100)}002\phantom{6}\\100\overline{)225}\\\phantom{100)}\underline{\phantom{}200\phantom{}}\\\phantom{100)9}25\\\end{array}
Find closest multiple of 100 to 225. We see that 2 \times 100 = 200 is the nearest. Now subtract 200 from 225 to get reminder 25. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }25
Since 25 is less than 100, stop the division. The reminder is 25. 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}