Evaluate
\frac{565}{3}\approx 188.333333333
Factor
\frac{5 \cdot 113}{3} = 188\frac{1}{3} = 188.33333333333334
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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)22600}\\\end{array}
Use the 1^{st} digit 2 from dividend 22600
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)22600}\\\end{array}
Since 2 is less than 120, use the next digit 2 from dividend 22600 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)22600}\\\end{array}
Use the 2^{nd} digit 2 from dividend 22600
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)22600}\\\end{array}
Since 22 is less than 120, use the next digit 6 from dividend 22600 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)22600}\\\end{array}
Use the 3^{rd} digit 6 from dividend 22600
\begin{array}{l}\phantom{120)}001\phantom{6}\\120\overline{)22600}\\\phantom{120)}\underline{\phantom{}120\phantom{99}}\\\phantom{120)}106\\\end{array}
Find closest multiple of 120 to 226. We see that 1 \times 120 = 120 is the nearest. Now subtract 120 from 226 to get reminder 106. Add 1 to quotient.
\begin{array}{l}\phantom{120)}001\phantom{7}\\120\overline{)22600}\\\phantom{120)}\underline{\phantom{}120\phantom{99}}\\\phantom{120)}1060\\\end{array}
Use the 4^{th} digit 0 from dividend 22600
\begin{array}{l}\phantom{120)}0018\phantom{8}\\120\overline{)22600}\\\phantom{120)}\underline{\phantom{}120\phantom{99}}\\\phantom{120)}1060\\\phantom{120)}\underline{\phantom{9}960\phantom{9}}\\\phantom{120)9}100\\\end{array}
Find closest multiple of 120 to 1060. We see that 8 \times 120 = 960 is the nearest. Now subtract 960 from 1060 to get reminder 100. Add 8 to quotient.
\begin{array}{l}\phantom{120)}0018\phantom{9}\\120\overline{)22600}\\\phantom{120)}\underline{\phantom{}120\phantom{99}}\\\phantom{120)}1060\\\phantom{120)}\underline{\phantom{9}960\phantom{9}}\\\phantom{120)9}1000\\\end{array}
Use the 5^{th} digit 0 from dividend 22600
\begin{array}{l}\phantom{120)}00188\phantom{10}\\120\overline{)22600}\\\phantom{120)}\underline{\phantom{}120\phantom{99}}\\\phantom{120)}1060\\\phantom{120)}\underline{\phantom{9}960\phantom{9}}\\\phantom{120)9}1000\\\phantom{120)}\underline{\phantom{99}960\phantom{}}\\\phantom{120)999}40\\\end{array}
Find closest multiple of 120 to 1000. We see that 8 \times 120 = 960 is the nearest. Now subtract 960 from 1000 to get reminder 40. Add 8 to quotient.
\text{Quotient: }188 \text{Reminder: }40
Since 40 is less than 120, stop the division. The reminder is 40. The topmost line 00188 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 188.
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}