Evaluate
\frac{25}{7}\approx 3.571428571
Factor
\frac{5 ^ {2}}{7} = 3\frac{4}{7} = 3.5714285714285716
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)125}\\\end{array}
Since 1 is less than 35, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)125}\\\end{array}
Since 12 is less than 35, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{35)}003\phantom{6}\\35\overline{)125}\\\phantom{35)}\underline{\phantom{}105\phantom{}}\\\phantom{35)9}20\\\end{array}
Find closest multiple of 35 to 125. We see that 3 \times 35 = 105 is the nearest. Now subtract 105 from 125 to get reminder 20. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }20
Since 20 is less than 35, stop the division. The reminder is 20. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}