Evaluate
\frac{4}{3}\approx 1.333333333
Factor
\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333
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\begin{array}{l}\phantom{480)}\phantom{1}\\480\overline{)640}\\\end{array}
Use the 1^{st} digit 6 from dividend 640
\begin{array}{l}\phantom{480)}0\phantom{2}\\480\overline{)640}\\\end{array}
Since 6 is less than 480, use the next digit 4 from dividend 640 and add 0 to the quotient
\begin{array}{l}\phantom{480)}0\phantom{3}\\480\overline{)640}\\\end{array}
Use the 2^{nd} digit 4 from dividend 640
\begin{array}{l}\phantom{480)}00\phantom{4}\\480\overline{)640}\\\end{array}
Since 64 is less than 480, use the next digit 0 from dividend 640 and add 0 to the quotient
\begin{array}{l}\phantom{480)}00\phantom{5}\\480\overline{)640}\\\end{array}
Use the 3^{rd} digit 0 from dividend 640
\begin{array}{l}\phantom{480)}001\phantom{6}\\480\overline{)640}\\\phantom{480)}\underline{\phantom{}480\phantom{}}\\\phantom{480)}160\\\end{array}
Find closest multiple of 480 to 640. We see that 1 \times 480 = 480 is the nearest. Now subtract 480 from 640 to get reminder 160. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }160
Since 160 is less than 480, stop the division. The reminder is 160. 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}