Evaluate
\frac{330}{157}\approx 2.101910828
Factor
\frac{2 \cdot 3 \cdot 5 \cdot 11}{157} = 2\frac{16}{157} = 2.1019108280254777
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\begin{array}{l}\phantom{3140)}\phantom{1}\\3140\overline{)6600}\\\end{array}
Use the 1^{st} digit 6 from dividend 6600
\begin{array}{l}\phantom{3140)}0\phantom{2}\\3140\overline{)6600}\\\end{array}
Since 6 is less than 3140, use the next digit 6 from dividend 6600 and add 0 to the quotient
\begin{array}{l}\phantom{3140)}0\phantom{3}\\3140\overline{)6600}\\\end{array}
Use the 2^{nd} digit 6 from dividend 6600
\begin{array}{l}\phantom{3140)}00\phantom{4}\\3140\overline{)6600}\\\end{array}
Since 66 is less than 3140, use the next digit 0 from dividend 6600 and add 0 to the quotient
\begin{array}{l}\phantom{3140)}00\phantom{5}\\3140\overline{)6600}\\\end{array}
Use the 3^{rd} digit 0 from dividend 6600
\begin{array}{l}\phantom{3140)}000\phantom{6}\\3140\overline{)6600}\\\end{array}
Since 660 is less than 3140, use the next digit 0 from dividend 6600 and add 0 to the quotient
\begin{array}{l}\phantom{3140)}000\phantom{7}\\3140\overline{)6600}\\\end{array}
Use the 4^{th} digit 0 from dividend 6600
\begin{array}{l}\phantom{3140)}0002\phantom{8}\\3140\overline{)6600}\\\phantom{3140)}\underline{\phantom{}6280\phantom{}}\\\phantom{3140)9}320\\\end{array}
Find closest multiple of 3140 to 6600. We see that 2 \times 3140 = 6280 is the nearest. Now subtract 6280 from 6600 to get reminder 320. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }320
Since 320 is less than 3140, stop the division. The reminder is 320. The topmost line 0002 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}