Evaluate
\frac{14}{5}=2.8
Factor
\frac{2 \cdot 7}{5} = 2\frac{4}{5} = 2.8
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\begin{array}{l}\phantom{205)}\phantom{1}\\205\overline{)574}\\\end{array}
Use the 1^{st} digit 5 from dividend 574
\begin{array}{l}\phantom{205)}0\phantom{2}\\205\overline{)574}\\\end{array}
Since 5 is less than 205, use the next digit 7 from dividend 574 and add 0 to the quotient
\begin{array}{l}\phantom{205)}0\phantom{3}\\205\overline{)574}\\\end{array}
Use the 2^{nd} digit 7 from dividend 574
\begin{array}{l}\phantom{205)}00\phantom{4}\\205\overline{)574}\\\end{array}
Since 57 is less than 205, use the next digit 4 from dividend 574 and add 0 to the quotient
\begin{array}{l}\phantom{205)}00\phantom{5}\\205\overline{)574}\\\end{array}
Use the 3^{rd} digit 4 from dividend 574
\begin{array}{l}\phantom{205)}002\phantom{6}\\205\overline{)574}\\\phantom{205)}\underline{\phantom{}410\phantom{}}\\\phantom{205)}164\\\end{array}
Find closest multiple of 205 to 574. We see that 2 \times 205 = 410 is the nearest. Now subtract 410 from 574 to get reminder 164. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }164
Since 164 is less than 205, stop the division. The reminder is 164. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}