Evaluate
\frac{71}{15}\approx 4.733333333
Factor
\frac{71}{3 \cdot 5} = 4\frac{11}{15} = 4.733333333333333
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)71}\\\end{array}
Use the 1^{st} digit 7 from dividend 71
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)71}\\\end{array}
Since 7 is less than 15, use the next digit 1 from dividend 71 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)71}\\\end{array}
Use the 2^{nd} digit 1 from dividend 71
\begin{array}{l}\phantom{15)}04\phantom{4}\\15\overline{)71}\\\phantom{15)}\underline{\phantom{}60\phantom{}}\\\phantom{15)}11\\\end{array}
Find closest multiple of 15 to 71. We see that 4 \times 15 = 60 is the nearest. Now subtract 60 from 71 to get reminder 11. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }11
Since 11 is less than 15, stop the division. The reminder is 11. 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}