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{140)}\phantom{1}\\140\overline{)500}\\\end{array}
Use the 1^{st} digit 5 from dividend 500
\begin{array}{l}\phantom{140)}0\phantom{2}\\140\overline{)500}\\\end{array}
Since 5 is less than 140, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{140)}0\phantom{3}\\140\overline{)500}\\\end{array}
Use the 2^{nd} digit 0 from dividend 500
\begin{array}{l}\phantom{140)}00\phantom{4}\\140\overline{)500}\\\end{array}
Since 50 is less than 140, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{140)}00\phantom{5}\\140\overline{)500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 500
\begin{array}{l}\phantom{140)}003\phantom{6}\\140\overline{)500}\\\phantom{140)}\underline{\phantom{}420\phantom{}}\\\phantom{140)9}80\\\end{array}
Find closest multiple of 140 to 500. We see that 3 \times 140 = 420 is the nearest. Now subtract 420 from 500 to get reminder 80. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }80
Since 80 is less than 140, stop the division. The reminder is 80. 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}