Evaluate
\frac{113}{25}=4.52
Factor
\frac{113}{5 ^ {2}} = 4\frac{13}{25} = 4.52
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)113}\\\end{array}
Use the 1^{st} digit 1 from dividend 113
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)113}\\\end{array}
Since 1 is less than 25, use the next digit 1 from dividend 113 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)113}\\\end{array}
Use the 2^{nd} digit 1 from dividend 113
\begin{array}{l}\phantom{25)}00\phantom{4}\\25\overline{)113}\\\end{array}
Since 11 is less than 25, use the next digit 3 from dividend 113 and add 0 to the quotient
\begin{array}{l}\phantom{25)}00\phantom{5}\\25\overline{)113}\\\end{array}
Use the 3^{rd} digit 3 from dividend 113
\begin{array}{l}\phantom{25)}004\phantom{6}\\25\overline{)113}\\\phantom{25)}\underline{\phantom{}100\phantom{}}\\\phantom{25)9}13\\\end{array}
Find closest multiple of 25 to 113. We see that 4 \times 25 = 100 is the nearest. Now subtract 100 from 113 to get reminder 13. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }13
Since 13 is less than 25, stop the division. The reminder is 13. 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}