Evaluate
\frac{370}{13}\approx 28.461538462
Factor
\frac{2 \cdot 5 \cdot 37}{13} = 28\frac{6}{13} = 28.46153846153846
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)1850}\\\end{array}
Use the 1^{st} digit 1 from dividend 1850
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)1850}\\\end{array}
Since 1 is less than 65, use the next digit 8 from dividend 1850 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)1850}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1850
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)1850}\\\end{array}
Since 18 is less than 65, use the next digit 5 from dividend 1850 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)1850}\\\end{array}
Use the 3^{rd} digit 5 from dividend 1850
\begin{array}{l}\phantom{65)}002\phantom{6}\\65\overline{)1850}\\\phantom{65)}\underline{\phantom{}130\phantom{9}}\\\phantom{65)9}55\\\end{array}
Find closest multiple of 65 to 185. We see that 2 \times 65 = 130 is the nearest. Now subtract 130 from 185 to get reminder 55. Add 2 to quotient.
\begin{array}{l}\phantom{65)}002\phantom{7}\\65\overline{)1850}\\\phantom{65)}\underline{\phantom{}130\phantom{9}}\\\phantom{65)9}550\\\end{array}
Use the 4^{th} digit 0 from dividend 1850
\begin{array}{l}\phantom{65)}0028\phantom{8}\\65\overline{)1850}\\\phantom{65)}\underline{\phantom{}130\phantom{9}}\\\phantom{65)9}550\\\phantom{65)}\underline{\phantom{9}520\phantom{}}\\\phantom{65)99}30\\\end{array}
Find closest multiple of 65 to 550. We see that 8 \times 65 = 520 is the nearest. Now subtract 520 from 550 to get reminder 30. Add 8 to quotient.
\text{Quotient: }28 \text{Reminder: }30
Since 30 is less than 65, stop the division. The reminder is 30. The topmost line 0028 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 28.
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}