Evaluate
\frac{110}{57}\approx 1.929824561
Factor
\frac{2 \cdot 5 \cdot 11}{3 \cdot 19} = 1\frac{53}{57} = 1.9298245614035088
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\begin{array}{l}\phantom{57)}\phantom{1}\\57\overline{)110}\\\end{array}
Use the 1^{st} digit 1 from dividend 110
\begin{array}{l}\phantom{57)}0\phantom{2}\\57\overline{)110}\\\end{array}
Since 1 is less than 57, use the next digit 1 from dividend 110 and add 0 to the quotient
\begin{array}{l}\phantom{57)}0\phantom{3}\\57\overline{)110}\\\end{array}
Use the 2^{nd} digit 1 from dividend 110
\begin{array}{l}\phantom{57)}00\phantom{4}\\57\overline{)110}\\\end{array}
Since 11 is less than 57, use the next digit 0 from dividend 110 and add 0 to the quotient
\begin{array}{l}\phantom{57)}00\phantom{5}\\57\overline{)110}\\\end{array}
Use the 3^{rd} digit 0 from dividend 110
\begin{array}{l}\phantom{57)}001\phantom{6}\\57\overline{)110}\\\phantom{57)}\underline{\phantom{9}57\phantom{}}\\\phantom{57)9}53\\\end{array}
Find closest multiple of 57 to 110. We see that 1 \times 57 = 57 is the nearest. Now subtract 57 from 110 to get reminder 53. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }53
Since 53 is less than 57, stop the division. The reminder is 53. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}