Evaluate
\frac{720}{169}\approx 4.26035503
Factor
\frac{2 ^ {4} \cdot 3 ^ {2} \cdot 5}{13 ^ {2}} = 4\frac{44}{169} = 4.260355029585799
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\begin{array}{l}\phantom{169)}\phantom{1}\\169\overline{)720}\\\end{array}
Use the 1^{st} digit 7 from dividend 720
\begin{array}{l}\phantom{169)}0\phantom{2}\\169\overline{)720}\\\end{array}
Since 7 is less than 169, use the next digit 2 from dividend 720 and add 0 to the quotient
\begin{array}{l}\phantom{169)}0\phantom{3}\\169\overline{)720}\\\end{array}
Use the 2^{nd} digit 2 from dividend 720
\begin{array}{l}\phantom{169)}00\phantom{4}\\169\overline{)720}\\\end{array}
Since 72 is less than 169, use the next digit 0 from dividend 720 and add 0 to the quotient
\begin{array}{l}\phantom{169)}00\phantom{5}\\169\overline{)720}\\\end{array}
Use the 3^{rd} digit 0 from dividend 720
\begin{array}{l}\phantom{169)}004\phantom{6}\\169\overline{)720}\\\phantom{169)}\underline{\phantom{}676\phantom{}}\\\phantom{169)9}44\\\end{array}
Find closest multiple of 169 to 720. We see that 4 \times 169 = 676 is the nearest. Now subtract 676 from 720 to get reminder 44. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }44
Since 44 is less than 169, stop the division. The reminder is 44. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}