Evaluate
\frac{8}{5}=1.6
Factor
\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)120}\\\end{array}
Use the 1^{st} digit 1 from dividend 120
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)120}\\\end{array}
Since 1 is less than 75, use the next digit 2 from dividend 120 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)120}\\\end{array}
Use the 2^{nd} digit 2 from dividend 120
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)120}\\\end{array}
Since 12 is less than 75, use the next digit 0 from dividend 120 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)120}\\\end{array}
Use the 3^{rd} digit 0 from dividend 120
\begin{array}{l}\phantom{75)}001\phantom{6}\\75\overline{)120}\\\phantom{75)}\underline{\phantom{9}75\phantom{}}\\\phantom{75)9}45\\\end{array}
Find closest multiple of 75 to 120. We see that 1 \times 75 = 75 is the nearest. Now subtract 75 from 120 to get reminder 45. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }45
Since 45 is less than 75, stop the division. The reminder is 45. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}