Evaluate
\frac{82}{45}\approx 1.822222222
Factor
\frac{2 \cdot 41}{3 ^ {2} \cdot 5} = 1\frac{37}{45} = 1.8222222222222222
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\begin{array}{l}\phantom{3600)}\phantom{1}\\3600\overline{)6560}\\\end{array}
Use the 1^{st} digit 6 from dividend 6560
\begin{array}{l}\phantom{3600)}0\phantom{2}\\3600\overline{)6560}\\\end{array}
Since 6 is less than 3600, use the next digit 5 from dividend 6560 and add 0 to the quotient
\begin{array}{l}\phantom{3600)}0\phantom{3}\\3600\overline{)6560}\\\end{array}
Use the 2^{nd} digit 5 from dividend 6560
\begin{array}{l}\phantom{3600)}00\phantom{4}\\3600\overline{)6560}\\\end{array}
Since 65 is less than 3600, use the next digit 6 from dividend 6560 and add 0 to the quotient
\begin{array}{l}\phantom{3600)}00\phantom{5}\\3600\overline{)6560}\\\end{array}
Use the 3^{rd} digit 6 from dividend 6560
\begin{array}{l}\phantom{3600)}000\phantom{6}\\3600\overline{)6560}\\\end{array}
Since 656 is less than 3600, use the next digit 0 from dividend 6560 and add 0 to the quotient
\begin{array}{l}\phantom{3600)}000\phantom{7}\\3600\overline{)6560}\\\end{array}
Use the 4^{th} digit 0 from dividend 6560
\begin{array}{l}\phantom{3600)}0001\phantom{8}\\3600\overline{)6560}\\\phantom{3600)}\underline{\phantom{}3600\phantom{}}\\\phantom{3600)}2960\\\end{array}
Find closest multiple of 3600 to 6560. We see that 1 \times 3600 = 3600 is the nearest. Now subtract 3600 from 6560 to get reminder 2960. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }2960
Since 2960 is less than 3600, stop the division. The reminder is 2960. The topmost line 0001 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}