Evaluate
\frac{16}{5}=3.2
Factor
\frac{2 ^ {4}}{5} = 3\frac{1}{5} = 3.2
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)240}\\\end{array}
Use the 1^{st} digit 2 from dividend 240
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)240}\\\end{array}
Since 2 is less than 75, use the next digit 4 from dividend 240 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)240}\\\end{array}
Use the 2^{nd} digit 4 from dividend 240
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)240}\\\end{array}
Since 24 is less than 75, use the next digit 0 from dividend 240 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)240}\\\end{array}
Use the 3^{rd} digit 0 from dividend 240
\begin{array}{l}\phantom{75)}003\phantom{6}\\75\overline{)240}\\\phantom{75)}\underline{\phantom{}225\phantom{}}\\\phantom{75)9}15\\\end{array}
Find closest multiple of 75 to 240. We see that 3 \times 75 = 225 is the nearest. Now subtract 225 from 240 to get reminder 15. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }15
Since 15 is less than 75, stop the division. The reminder is 15. 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}