Evaluate
\frac{194}{101}\approx 1.920792079
Factor
\frac{2 \cdot 97}{101} = 1\frac{93}{101} = 1.9207920792079207
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\begin{array}{l}\phantom{101)}\phantom{1}\\101\overline{)194}\\\end{array}
Use the 1^{st} digit 1 from dividend 194
\begin{array}{l}\phantom{101)}0\phantom{2}\\101\overline{)194}\\\end{array}
Since 1 is less than 101, use the next digit 9 from dividend 194 and add 0 to the quotient
\begin{array}{l}\phantom{101)}0\phantom{3}\\101\overline{)194}\\\end{array}
Use the 2^{nd} digit 9 from dividend 194
\begin{array}{l}\phantom{101)}00\phantom{4}\\101\overline{)194}\\\end{array}
Since 19 is less than 101, use the next digit 4 from dividend 194 and add 0 to the quotient
\begin{array}{l}\phantom{101)}00\phantom{5}\\101\overline{)194}\\\end{array}
Use the 3^{rd} digit 4 from dividend 194
\begin{array}{l}\phantom{101)}001\phantom{6}\\101\overline{)194}\\\phantom{101)}\underline{\phantom{}101\phantom{}}\\\phantom{101)9}93\\\end{array}
Find closest multiple of 101 to 194. We see that 1 \times 101 = 101 is the nearest. Now subtract 101 from 194 to get reminder 93. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }93
Since 93 is less than 101, stop the division. The reminder is 93. 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}