Evaluate
\frac{106}{25}=4.24
Factor
\frac{2 \cdot 53}{5 ^ {2}} = 4\frac{6}{25} = 4.24
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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)530}\\\end{array}
Use the 1^{st} digit 5 from dividend 530
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)530}\\\end{array}
Since 5 is less than 125, use the next digit 3 from dividend 530 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)530}\\\end{array}
Use the 2^{nd} digit 3 from dividend 530
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)530}\\\end{array}
Since 53 is less than 125, use the next digit 0 from dividend 530 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)530}\\\end{array}
Use the 3^{rd} digit 0 from dividend 530
\begin{array}{l}\phantom{125)}004\phantom{6}\\125\overline{)530}\\\phantom{125)}\underline{\phantom{}500\phantom{}}\\\phantom{125)9}30\\\end{array}
Find closest multiple of 125 to 530. We see that 4 \times 125 = 500 is the nearest. Now subtract 500 from 530 to get reminder 30. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }30
Since 30 is less than 125, stop the division. The reminder is 30. 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}