Evaluate
\frac{142}{25}=5.68
Factor
\frac{2 \cdot 71}{5 ^ {2}} = 5\frac{17}{25} = 5.68
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)142}\\\end{array}
Use the 1^{st} digit 1 from dividend 142
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)142}\\\end{array}
Since 1 is less than 25, use the next digit 4 from dividend 142 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)142}\\\end{array}
Use the 2^{nd} digit 4 from dividend 142
\begin{array}{l}\phantom{25)}00\phantom{4}\\25\overline{)142}\\\end{array}
Since 14 is less than 25, use the next digit 2 from dividend 142 and add 0 to the quotient
\begin{array}{l}\phantom{25)}00\phantom{5}\\25\overline{)142}\\\end{array}
Use the 3^{rd} digit 2 from dividend 142
\begin{array}{l}\phantom{25)}005\phantom{6}\\25\overline{)142}\\\phantom{25)}\underline{\phantom{}125\phantom{}}\\\phantom{25)9}17\\\end{array}
Find closest multiple of 25 to 142. We see that 5 \times 25 = 125 is the nearest. Now subtract 125 from 142 to get reminder 17. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }17
Since 17 is less than 25, stop the division. The reminder is 17. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}