Evaluate
\frac{5}{3}\approx 1.666666667
Factor
\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)125}\\\end{array}
Since 1 is less than 75, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)125}\\\end{array}
Since 12 is less than 75, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{75)}001\phantom{6}\\75\overline{)125}\\\phantom{75)}\underline{\phantom{9}75\phantom{}}\\\phantom{75)9}50\\\end{array}
Find closest multiple of 75 to 125. We see that 1 \times 75 = 75 is the nearest. Now subtract 75 from 125 to get reminder 50. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }50
Since 50 is less than 75, stop the division. The reminder is 50. 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}