Evaluate
\frac{223}{44}\approx 5.068181818
Factor
\frac{223}{2 ^ {2} \cdot 11} = 5\frac{3}{44} = 5.068181818181818
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\begin{array}{l}\phantom{44)}\phantom{1}\\44\overline{)223}\\\end{array}
Use the 1^{st} digit 2 from dividend 223
\begin{array}{l}\phantom{44)}0\phantom{2}\\44\overline{)223}\\\end{array}
Since 2 is less than 44, use the next digit 2 from dividend 223 and add 0 to the quotient
\begin{array}{l}\phantom{44)}0\phantom{3}\\44\overline{)223}\\\end{array}
Use the 2^{nd} digit 2 from dividend 223
\begin{array}{l}\phantom{44)}00\phantom{4}\\44\overline{)223}\\\end{array}
Since 22 is less than 44, use the next digit 3 from dividend 223 and add 0 to the quotient
\begin{array}{l}\phantom{44)}00\phantom{5}\\44\overline{)223}\\\end{array}
Use the 3^{rd} digit 3 from dividend 223
\begin{array}{l}\phantom{44)}005\phantom{6}\\44\overline{)223}\\\phantom{44)}\underline{\phantom{}220\phantom{}}\\\phantom{44)99}3\\\end{array}
Find closest multiple of 44 to 223. We see that 5 \times 44 = 220 is the nearest. Now subtract 220 from 223 to get reminder 3. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }3
Since 3 is less than 44, stop the division. The reminder is 3. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
Examples
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{ 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}