Evaluate
\frac{19999}{3}\approx 6666.333333333
Factor
\frac{7 \cdot 2857}{3} = 6666\frac{1}{3} = 6666.333333333333
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)99995}\\\end{array}
Use the 1^{st} digit 9 from dividend 99995
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)99995}\\\end{array}
Since 9 is less than 15, use the next digit 9 from dividend 99995 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)99995}\\\end{array}
Use the 2^{nd} digit 9 from dividend 99995
\begin{array}{l}\phantom{15)}06\phantom{4}\\15\overline{)99995}\\\phantom{15)}\underline{\phantom{}90\phantom{999}}\\\phantom{15)9}9\\\end{array}
Find closest multiple of 15 to 99. We see that 6 \times 15 = 90 is the nearest. Now subtract 90 from 99 to get reminder 9. Add 6 to quotient.
\begin{array}{l}\phantom{15)}06\phantom{5}\\15\overline{)99995}\\\phantom{15)}\underline{\phantom{}90\phantom{999}}\\\phantom{15)9}99\\\end{array}
Use the 3^{rd} digit 9 from dividend 99995
\begin{array}{l}\phantom{15)}066\phantom{6}\\15\overline{)99995}\\\phantom{15)}\underline{\phantom{}90\phantom{999}}\\\phantom{15)9}99\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)99}9\\\end{array}
Find closest multiple of 15 to 99. We see that 6 \times 15 = 90 is the nearest. Now subtract 90 from 99 to get reminder 9. Add 6 to quotient.
\begin{array}{l}\phantom{15)}066\phantom{7}\\15\overline{)99995}\\\phantom{15)}\underline{\phantom{}90\phantom{999}}\\\phantom{15)9}99\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)99}99\\\end{array}
Use the 4^{th} digit 9 from dividend 99995
\begin{array}{l}\phantom{15)}0666\phantom{8}\\15\overline{)99995}\\\phantom{15)}\underline{\phantom{}90\phantom{999}}\\\phantom{15)9}99\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)99}99\\\phantom{15)}\underline{\phantom{99}90\phantom{9}}\\\phantom{15)999}9\\\end{array}
Find closest multiple of 15 to 99. We see that 6 \times 15 = 90 is the nearest. Now subtract 90 from 99 to get reminder 9. Add 6 to quotient.
\begin{array}{l}\phantom{15)}0666\phantom{9}\\15\overline{)99995}\\\phantom{15)}\underline{\phantom{}90\phantom{999}}\\\phantom{15)9}99\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)99}99\\\phantom{15)}\underline{\phantom{99}90\phantom{9}}\\\phantom{15)999}95\\\end{array}
Use the 5^{th} digit 5 from dividend 99995
\begin{array}{l}\phantom{15)}06666\phantom{10}\\15\overline{)99995}\\\phantom{15)}\underline{\phantom{}90\phantom{999}}\\\phantom{15)9}99\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)99}99\\\phantom{15)}\underline{\phantom{99}90\phantom{9}}\\\phantom{15)999}95\\\phantom{15)}\underline{\phantom{999}90\phantom{}}\\\phantom{15)9999}5\\\end{array}
Find closest multiple of 15 to 95. We see that 6 \times 15 = 90 is the nearest. Now subtract 90 from 95 to get reminder 5. Add 6 to quotient.
\text{Quotient: }6666 \text{Reminder: }5
Since 5 is less than 15, stop the division. The reminder is 5. The topmost line 06666 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6666.
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}