Evaluate
\frac{212}{145}\approx 1.462068966
Factor
\frac{2 ^ {2} \cdot 53}{5 \cdot 29} = 1\frac{67}{145} = 1.4620689655172414
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\begin{array}{l}\phantom{145)}\phantom{1}\\145\overline{)212}\\\end{array}
Use the 1^{st} digit 2 from dividend 212
\begin{array}{l}\phantom{145)}0\phantom{2}\\145\overline{)212}\\\end{array}
Since 2 is less than 145, use the next digit 1 from dividend 212 and add 0 to the quotient
\begin{array}{l}\phantom{145)}0\phantom{3}\\145\overline{)212}\\\end{array}
Use the 2^{nd} digit 1 from dividend 212
\begin{array}{l}\phantom{145)}00\phantom{4}\\145\overline{)212}\\\end{array}
Since 21 is less than 145, use the next digit 2 from dividend 212 and add 0 to the quotient
\begin{array}{l}\phantom{145)}00\phantom{5}\\145\overline{)212}\\\end{array}
Use the 3^{rd} digit 2 from dividend 212
\begin{array}{l}\phantom{145)}001\phantom{6}\\145\overline{)212}\\\phantom{145)}\underline{\phantom{}145\phantom{}}\\\phantom{145)9}67\\\end{array}
Find closest multiple of 145 to 212. We see that 1 \times 145 = 145 is the nearest. Now subtract 145 from 212 to get reminder 67. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }67
Since 67 is less than 145, stop the division. The reminder is 67. 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}