Evaluate
\frac{110}{21}\approx 5.238095238
Factor
\frac{2 \cdot 5 \cdot 11}{3 \cdot 7} = 5\frac{5}{21} = 5.238095238095238
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\begin{array}{l}\phantom{105)}\phantom{1}\\105\overline{)550}\\\end{array}
Use the 1^{st} digit 5 from dividend 550
\begin{array}{l}\phantom{105)}0\phantom{2}\\105\overline{)550}\\\end{array}
Since 5 is less than 105, use the next digit 5 from dividend 550 and add 0 to the quotient
\begin{array}{l}\phantom{105)}0\phantom{3}\\105\overline{)550}\\\end{array}
Use the 2^{nd} digit 5 from dividend 550
\begin{array}{l}\phantom{105)}00\phantom{4}\\105\overline{)550}\\\end{array}
Since 55 is less than 105, use the next digit 0 from dividend 550 and add 0 to the quotient
\begin{array}{l}\phantom{105)}00\phantom{5}\\105\overline{)550}\\\end{array}
Use the 3^{rd} digit 0 from dividend 550
\begin{array}{l}\phantom{105)}005\phantom{6}\\105\overline{)550}\\\phantom{105)}\underline{\phantom{}525\phantom{}}\\\phantom{105)9}25\\\end{array}
Find closest multiple of 105 to 550. We see that 5 \times 105 = 525 is the nearest. Now subtract 525 from 550 to get reminder 25. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }25
Since 25 is less than 105, stop the division. The reminder is 25. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}