Evaluate
\frac{49}{20}=2.45
Factor
\frac{7 ^ {2}}{2 ^ {2} \cdot 5} = 2\frac{9}{20} = 2.45
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)245}\\\end{array}
Use the 1^{st} digit 2 from dividend 245
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)245}\\\end{array}
Since 2 is less than 100, use the next digit 4 from dividend 245 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)245}\\\end{array}
Use the 2^{nd} digit 4 from dividend 245
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)245}\\\end{array}
Since 24 is less than 100, use the next digit 5 from dividend 245 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)245}\\\end{array}
Use the 3^{rd} digit 5 from dividend 245
\begin{array}{l}\phantom{100)}002\phantom{6}\\100\overline{)245}\\\phantom{100)}\underline{\phantom{}200\phantom{}}\\\phantom{100)9}45\\\end{array}
Find closest multiple of 100 to 245. We see that 2 \times 100 = 200 is the nearest. Now subtract 200 from 245 to get reminder 45. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }45
Since 45 is less than 100, stop the division. The reminder is 45. 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}