Evaluate
\frac{16}{3}\approx 5.333333333
Factor
\frac{2 ^ {4}}{3} = 5\frac{1}{3} = 5.333333333333333
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)160}\\\end{array}
Use the 1^{st} digit 1 from dividend 160
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)160}\\\end{array}
Since 1 is less than 30, use the next digit 6 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)160}\\\end{array}
Use the 2^{nd} digit 6 from dividend 160
\begin{array}{l}\phantom{30)}00\phantom{4}\\30\overline{)160}\\\end{array}
Since 16 is less than 30, use the next digit 0 from dividend 160 and add 0 to the quotient
\begin{array}{l}\phantom{30)}00\phantom{5}\\30\overline{)160}\\\end{array}
Use the 3^{rd} digit 0 from dividend 160
\begin{array}{l}\phantom{30)}005\phantom{6}\\30\overline{)160}\\\phantom{30)}\underline{\phantom{}150\phantom{}}\\\phantom{30)9}10\\\end{array}
Find closest multiple of 30 to 160. We see that 5 \times 30 = 150 is the nearest. Now subtract 150 from 160 to get reminder 10. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }10
Since 10 is less than 30, stop the division. The reminder is 10. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}