Evaluate
\frac{160}{81}\approx 1.975308642
Factor
\frac{2 ^ {5} \cdot 5}{3 ^ {4}} = 1\frac{79}{81} = 1.9753086419753085
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\begin{array}{l}\phantom{162)}\phantom{1}\\162\overline{)320}\\\end{array}
Use the 1^{st} digit 3 from dividend 320
\begin{array}{l}\phantom{162)}0\phantom{2}\\162\overline{)320}\\\end{array}
Since 3 is less than 162, use the next digit 2 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{162)}0\phantom{3}\\162\overline{)320}\\\end{array}
Use the 2^{nd} digit 2 from dividend 320
\begin{array}{l}\phantom{162)}00\phantom{4}\\162\overline{)320}\\\end{array}
Since 32 is less than 162, use the next digit 0 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{162)}00\phantom{5}\\162\overline{)320}\\\end{array}
Use the 3^{rd} digit 0 from dividend 320
\begin{array}{l}\phantom{162)}001\phantom{6}\\162\overline{)320}\\\phantom{162)}\underline{\phantom{}162\phantom{}}\\\phantom{162)}158\\\end{array}
Find closest multiple of 162 to 320. We see that 1 \times 162 = 162 is the nearest. Now subtract 162 from 320 to get reminder 158. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }158
Since 158 is less than 162, stop the division. The reminder is 158. 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}