Evaluate
\frac{68}{53}\approx 1.283018868
Factor
\frac{2 ^ {2} \cdot 17}{53} = 1\frac{15}{53} = 1.2830188679245282
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\begin{array}{l}\phantom{212)}\phantom{1}\\212\overline{)272}\\\end{array}
Use the 1^{st} digit 2 from dividend 272
\begin{array}{l}\phantom{212)}0\phantom{2}\\212\overline{)272}\\\end{array}
Since 2 is less than 212, use the next digit 7 from dividend 272 and add 0 to the quotient
\begin{array}{l}\phantom{212)}0\phantom{3}\\212\overline{)272}\\\end{array}
Use the 2^{nd} digit 7 from dividend 272
\begin{array}{l}\phantom{212)}00\phantom{4}\\212\overline{)272}\\\end{array}
Since 27 is less than 212, use the next digit 2 from dividend 272 and add 0 to the quotient
\begin{array}{l}\phantom{212)}00\phantom{5}\\212\overline{)272}\\\end{array}
Use the 3^{rd} digit 2 from dividend 272
\begin{array}{l}\phantom{212)}001\phantom{6}\\212\overline{)272}\\\phantom{212)}\underline{\phantom{}212\phantom{}}\\\phantom{212)9}60\\\end{array}
Find closest multiple of 212 to 272. We see that 1 \times 212 = 212 is the nearest. Now subtract 212 from 272 to get reminder 60. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }60
Since 60 is less than 212, stop the division. The reminder is 60. 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}