Evaluate
\frac{119}{13}\approx 9.153846154
Factor
\frac{7 \cdot 17}{13} = 9\frac{2}{13} = 9.153846153846153
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)119}\\\end{array}
Use the 1^{st} digit 1 from dividend 119
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)119}\\\end{array}
Since 1 is less than 13, use the next digit 1 from dividend 119 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)119}\\\end{array}
Use the 2^{nd} digit 1 from dividend 119
\begin{array}{l}\phantom{13)}00\phantom{4}\\13\overline{)119}\\\end{array}
Since 11 is less than 13, use the next digit 9 from dividend 119 and add 0 to the quotient
\begin{array}{l}\phantom{13)}00\phantom{5}\\13\overline{)119}\\\end{array}
Use the 3^{rd} digit 9 from dividend 119
\begin{array}{l}\phantom{13)}009\phantom{6}\\13\overline{)119}\\\phantom{13)}\underline{\phantom{}117\phantom{}}\\\phantom{13)99}2\\\end{array}
Find closest multiple of 13 to 119. We see that 9 \times 13 = 117 is the nearest. Now subtract 117 from 119 to get reminder 2. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }2
Since 2 is less than 13, stop the division. The reminder is 2. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}