Evaluate
\frac{157777}{11}\approx 14343.363636364
Factor
\frac{17 \cdot 9281}{11} = 14343\frac{4}{11} = 14343.363636363636
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)788885}\\\end{array}
Use the 1^{st} digit 7 from dividend 788885
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)788885}\\\end{array}
Since 7 is less than 55, use the next digit 8 from dividend 788885 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)788885}\\\end{array}
Use the 2^{nd} digit 8 from dividend 788885
\begin{array}{l}\phantom{55)}01\phantom{4}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}23\\\end{array}
Find closest multiple of 55 to 78. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 78 to get reminder 23. Add 1 to quotient.
\begin{array}{l}\phantom{55)}01\phantom{5}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\end{array}
Use the 3^{rd} digit 8 from dividend 788885
\begin{array}{l}\phantom{55)}014\phantom{6}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\phantom{55)}\underline{\phantom{}220\phantom{999}}\\\phantom{55)9}18\\\end{array}
Find closest multiple of 55 to 238. We see that 4 \times 55 = 220 is the nearest. Now subtract 220 from 238 to get reminder 18. Add 4 to quotient.
\begin{array}{l}\phantom{55)}014\phantom{7}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\phantom{55)}\underline{\phantom{}220\phantom{999}}\\\phantom{55)9}188\\\end{array}
Use the 4^{th} digit 8 from dividend 788885
\begin{array}{l}\phantom{55)}0143\phantom{8}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\phantom{55)}\underline{\phantom{}220\phantom{999}}\\\phantom{55)9}188\\\phantom{55)}\underline{\phantom{9}165\phantom{99}}\\\phantom{55)99}23\\\end{array}
Find closest multiple of 55 to 188. We see that 3 \times 55 = 165 is the nearest. Now subtract 165 from 188 to get reminder 23. Add 3 to quotient.
\begin{array}{l}\phantom{55)}0143\phantom{9}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\phantom{55)}\underline{\phantom{}220\phantom{999}}\\\phantom{55)9}188\\\phantom{55)}\underline{\phantom{9}165\phantom{99}}\\\phantom{55)99}238\\\end{array}
Use the 5^{th} digit 8 from dividend 788885
\begin{array}{l}\phantom{55)}01434\phantom{10}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\phantom{55)}\underline{\phantom{}220\phantom{999}}\\\phantom{55)9}188\\\phantom{55)}\underline{\phantom{9}165\phantom{99}}\\\phantom{55)99}238\\\phantom{55)}\underline{\phantom{99}220\phantom{9}}\\\phantom{55)999}18\\\end{array}
Find closest multiple of 55 to 238. We see that 4 \times 55 = 220 is the nearest. Now subtract 220 from 238 to get reminder 18. Add 4 to quotient.
\begin{array}{l}\phantom{55)}01434\phantom{11}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\phantom{55)}\underline{\phantom{}220\phantom{999}}\\\phantom{55)9}188\\\phantom{55)}\underline{\phantom{9}165\phantom{99}}\\\phantom{55)99}238\\\phantom{55)}\underline{\phantom{99}220\phantom{9}}\\\phantom{55)999}185\\\end{array}
Use the 6^{th} digit 5 from dividend 788885
\begin{array}{l}\phantom{55)}014343\phantom{12}\\55\overline{)788885}\\\phantom{55)}\underline{\phantom{}55\phantom{9999}}\\\phantom{55)}238\\\phantom{55)}\underline{\phantom{}220\phantom{999}}\\\phantom{55)9}188\\\phantom{55)}\underline{\phantom{9}165\phantom{99}}\\\phantom{55)99}238\\\phantom{55)}\underline{\phantom{99}220\phantom{9}}\\\phantom{55)999}185\\\phantom{55)}\underline{\phantom{999}165\phantom{}}\\\phantom{55)9999}20\\\end{array}
Find closest multiple of 55 to 185. We see that 3 \times 55 = 165 is the nearest. Now subtract 165 from 185 to get reminder 20. Add 3 to quotient.
\text{Quotient: }14343 \text{Reminder: }20
Since 20 is less than 55, stop the division. The reminder is 20. The topmost line 014343 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 14343.
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}