Evaluate
\frac{4}{3}\approx 1.333333333
Factor
\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)84}\\\end{array}
Use the 1^{st} digit 8 from dividend 84
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)84}\\\end{array}
Since 8 is less than 63, use the next digit 4 from dividend 84 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)84}\\\end{array}
Use the 2^{nd} digit 4 from dividend 84
\begin{array}{l}\phantom{63)}01\phantom{4}\\63\overline{)84}\\\phantom{63)}\underline{\phantom{}63\phantom{}}\\\phantom{63)}21\\\end{array}
Find closest multiple of 63 to 84. We see that 1 \times 63 = 63 is the nearest. Now subtract 63 from 84 to get reminder 21. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }21
Since 21 is less than 63, stop the division. The reminder is 21. The topmost line 01 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}