Evaluate
\frac{19}{10}=1.9
Factor
\frac{19}{2 \cdot 5} = 1\frac{9}{10} = 1.9
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)171}\\\end{array}
Use the 1^{st} digit 1 from dividend 171
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)171}\\\end{array}
Since 1 is less than 90, use the next digit 7 from dividend 171 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)171}\\\end{array}
Use the 2^{nd} digit 7 from dividend 171
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)171}\\\end{array}
Since 17 is less than 90, use the next digit 1 from dividend 171 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)171}\\\end{array}
Use the 3^{rd} digit 1 from dividend 171
\begin{array}{l}\phantom{90)}001\phantom{6}\\90\overline{)171}\\\phantom{90)}\underline{\phantom{9}90\phantom{}}\\\phantom{90)9}81\\\end{array}
Find closest multiple of 90 to 171. We see that 1 \times 90 = 90 is the nearest. Now subtract 90 from 171 to get reminder 81. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }81
Since 81 is less than 90, stop the division. The reminder is 81. 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}