Evaluate
\frac{5}{3}\approx 1.666666667
Factor
\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667
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\begin{array}{l}\phantom{270)}\phantom{1}\\270\overline{)450}\\\end{array}
Use the 1^{st} digit 4 from dividend 450
\begin{array}{l}\phantom{270)}0\phantom{2}\\270\overline{)450}\\\end{array}
Since 4 is less than 270, use the next digit 5 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{270)}0\phantom{3}\\270\overline{)450}\\\end{array}
Use the 2^{nd} digit 5 from dividend 450
\begin{array}{l}\phantom{270)}00\phantom{4}\\270\overline{)450}\\\end{array}
Since 45 is less than 270, use the next digit 0 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{270)}00\phantom{5}\\270\overline{)450}\\\end{array}
Use the 3^{rd} digit 0 from dividend 450
\begin{array}{l}\phantom{270)}001\phantom{6}\\270\overline{)450}\\\phantom{270)}\underline{\phantom{}270\phantom{}}\\\phantom{270)}180\\\end{array}
Find closest multiple of 270 to 450. We see that 1 \times 270 = 270 is the nearest. Now subtract 270 from 450 to get reminder 180. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }180
Since 180 is less than 270, stop the division. The reminder is 180. 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}