Evaluate
\frac{7}{3}\approx 2.333333333
Factor
\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)140}\\\end{array}
Use the 1^{st} digit 1 from dividend 140
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)140}\\\end{array}
Since 1 is less than 60, use the next digit 4 from dividend 140 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)140}\\\end{array}
Use the 2^{nd} digit 4 from dividend 140
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)140}\\\end{array}
Since 14 is less than 60, use the next digit 0 from dividend 140 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)140}\\\end{array}
Use the 3^{rd} digit 0 from dividend 140
\begin{array}{l}\phantom{60)}002\phantom{6}\\60\overline{)140}\\\phantom{60)}\underline{\phantom{}120\phantom{}}\\\phantom{60)9}20\\\end{array}
Find closest multiple of 60 to 140. We see that 2 \times 60 = 120 is the nearest. Now subtract 120 from 140 to get reminder 20. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }20
Since 20 is less than 60, stop the division. The reminder is 20. 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}