Evaluate
\frac{109}{25}=4.36
Factor
\frac{109}{5 ^ {2}} = 4\frac{9}{25} = 4.36
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)436}\\\end{array}
Use the 1^{st} digit 4 from dividend 436
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)436}\\\end{array}
Since 4 is less than 100, use the next digit 3 from dividend 436 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)436}\\\end{array}
Use the 2^{nd} digit 3 from dividend 436
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)436}\\\end{array}
Since 43 is less than 100, use the next digit 6 from dividend 436 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)436}\\\end{array}
Use the 3^{rd} digit 6 from dividend 436
\begin{array}{l}\phantom{100)}004\phantom{6}\\100\overline{)436}\\\phantom{100)}\underline{\phantom{}400\phantom{}}\\\phantom{100)9}36\\\end{array}
Find closest multiple of 100 to 436. We see that 4 \times 100 = 400 is the nearest. Now subtract 400 from 436 to get reminder 36. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }36
Since 36 is less than 100, stop the division. The reminder is 36. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}