Evaluate
\frac{13}{3}\approx 4.333333333
Factor
\frac{13}{3} = 4\frac{1}{3} = 4.333333333333333
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)78}\\\end{array}
Since 7 is less than 18, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{18)}04\phantom{4}\\18\overline{)78}\\\phantom{18)}\underline{\phantom{}72\phantom{}}\\\phantom{18)9}6\\\end{array}
Find closest multiple of 18 to 78. We see that 4 \times 18 = 72 is the nearest. Now subtract 72 from 78 to get reminder 6. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }6
Since 6 is less than 18, stop the division. The reminder is 6. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}