Evaluate
\frac{777611}{5}=155522.2
Factor
\frac{389 \cdot 1999}{5} = 155522\frac{1}{5} = 155522.2
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)1555222}\\\end{array}
Use the 1^{st} digit 1 from dividend 1555222
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)1555222}\\\end{array}
Since 1 is less than 10, use the next digit 5 from dividend 1555222 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)1555222}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1555222
\begin{array}{l}\phantom{10)}01\phantom{4}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}5\\\end{array}
Find closest multiple of 10 to 15. We see that 1 \times 10 = 10 is the nearest. Now subtract 10 from 15 to get reminder 5. Add 1 to quotient.
\begin{array}{l}\phantom{10)}01\phantom{5}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\end{array}
Use the 3^{rd} digit 5 from dividend 1555222
\begin{array}{l}\phantom{10)}015\phantom{6}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}5\\\end{array}
Find closest multiple of 10 to 55. We see that 5 \times 10 = 50 is the nearest. Now subtract 50 from 55 to get reminder 5. Add 5 to quotient.
\begin{array}{l}\phantom{10)}015\phantom{7}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\end{array}
Use the 4^{th} digit 5 from dividend 1555222
\begin{array}{l}\phantom{10)}0155\phantom{8}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\phantom{10)}\underline{\phantom{99}50\phantom{999}}\\\phantom{10)999}5\\\end{array}
Find closest multiple of 10 to 55. We see that 5 \times 10 = 50 is the nearest. Now subtract 50 from 55 to get reminder 5. Add 5 to quotient.
\begin{array}{l}\phantom{10)}0155\phantom{9}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\phantom{10)}\underline{\phantom{99}50\phantom{999}}\\\phantom{10)999}52\\\end{array}
Use the 5^{th} digit 2 from dividend 1555222
\begin{array}{l}\phantom{10)}01555\phantom{10}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\phantom{10)}\underline{\phantom{99}50\phantom{999}}\\\phantom{10)999}52\\\phantom{10)}\underline{\phantom{999}50\phantom{99}}\\\phantom{10)9999}2\\\end{array}
Find closest multiple of 10 to 52. We see that 5 \times 10 = 50 is the nearest. Now subtract 50 from 52 to get reminder 2. Add 5 to quotient.
\begin{array}{l}\phantom{10)}01555\phantom{11}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\phantom{10)}\underline{\phantom{99}50\phantom{999}}\\\phantom{10)999}52\\\phantom{10)}\underline{\phantom{999}50\phantom{99}}\\\phantom{10)9999}22\\\end{array}
Use the 6^{th} digit 2 from dividend 1555222
\begin{array}{l}\phantom{10)}015552\phantom{12}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\phantom{10)}\underline{\phantom{99}50\phantom{999}}\\\phantom{10)999}52\\\phantom{10)}\underline{\phantom{999}50\phantom{99}}\\\phantom{10)9999}22\\\phantom{10)}\underline{\phantom{9999}20\phantom{9}}\\\phantom{10)99999}2\\\end{array}
Find closest multiple of 10 to 22. We see that 2 \times 10 = 20 is the nearest. Now subtract 20 from 22 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{10)}015552\phantom{13}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\phantom{10)}\underline{\phantom{99}50\phantom{999}}\\\phantom{10)999}52\\\phantom{10)}\underline{\phantom{999}50\phantom{99}}\\\phantom{10)9999}22\\\phantom{10)}\underline{\phantom{9999}20\phantom{9}}\\\phantom{10)99999}22\\\end{array}
Use the 7^{th} digit 2 from dividend 1555222
\begin{array}{l}\phantom{10)}0155522\phantom{14}\\10\overline{)1555222}\\\phantom{10)}\underline{\phantom{}10\phantom{99999}}\\\phantom{10)9}55\\\phantom{10)}\underline{\phantom{9}50\phantom{9999}}\\\phantom{10)99}55\\\phantom{10)}\underline{\phantom{99}50\phantom{999}}\\\phantom{10)999}52\\\phantom{10)}\underline{\phantom{999}50\phantom{99}}\\\phantom{10)9999}22\\\phantom{10)}\underline{\phantom{9999}20\phantom{9}}\\\phantom{10)99999}22\\\phantom{10)}\underline{\phantom{99999}20\phantom{}}\\\phantom{10)999999}2\\\end{array}
Find closest multiple of 10 to 22. We see that 2 \times 10 = 20 is the nearest. Now subtract 20 from 22 to get reminder 2. Add 2 to quotient.
\text{Quotient: }155522 \text{Reminder: }2
Since 2 is less than 10, stop the division. The reminder is 2. The topmost line 0155522 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 155522.
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}