Evaluate
\frac{65}{3}\approx 21.666666667
Factor
\frac{5 \cdot 13}{3} = 21\frac{2}{3} = 21.666666666666668
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)260}\\\end{array}
Use the 1^{st} digit 2 from dividend 260
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)260}\\\end{array}
Since 2 is less than 12, use the next digit 6 from dividend 260 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)260}\\\end{array}
Use the 2^{nd} digit 6 from dividend 260
\begin{array}{l}\phantom{12)}02\phantom{4}\\12\overline{)260}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}2\\\end{array}
Find closest multiple of 12 to 26. We see that 2 \times 12 = 24 is the nearest. Now subtract 24 from 26 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{12)}02\phantom{5}\\12\overline{)260}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}20\\\end{array}
Use the 3^{rd} digit 0 from dividend 260
\begin{array}{l}\phantom{12)}021\phantom{6}\\12\overline{)260}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}20\\\phantom{12)}\underline{\phantom{9}12\phantom{}}\\\phantom{12)99}8\\\end{array}
Find closest multiple of 12 to 20. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 20 to get reminder 8. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }8
Since 8 is less than 12, stop the division. The reminder is 8. The topmost line 021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}