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{90)}\phantom{1}\\90\overline{)150}\\\end{array}
Use the 1^{st} digit 1 from dividend 150
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)150}\\\end{array}
Since 1 is less than 90, use the next digit 5 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)150}\\\end{array}
Use the 2^{nd} digit 5 from dividend 150
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)150}\\\end{array}
Since 15 is less than 90, use the next digit 0 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)150}\\\end{array}
Use the 3^{rd} digit 0 from dividend 150
\begin{array}{l}\phantom{90)}001\phantom{6}\\90\overline{)150}\\\phantom{90)}\underline{\phantom{9}90\phantom{}}\\\phantom{90)9}60\\\end{array}
Find closest multiple of 90 to 150. We see that 1 \times 90 = 90 is the nearest. Now subtract 90 from 150 to get reminder 60. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }60
Since 60 is less than 90, stop the division. The reminder is 60. 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}