Evaluate
\frac{64}{3}\approx 21.333333333
Factor
\frac{2 ^ {6}}{3} = 21\frac{1}{3} = 21.333333333333332
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)320}\\\end{array}
Use the 1^{st} digit 3 from dividend 320
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)320}\\\end{array}
Since 3 is less than 15, use the next digit 2 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)320}\\\end{array}
Use the 2^{nd} digit 2 from dividend 320
\begin{array}{l}\phantom{15)}02\phantom{4}\\15\overline{)320}\\\phantom{15)}\underline{\phantom{}30\phantom{9}}\\\phantom{15)9}2\\\end{array}
Find closest multiple of 15 to 32. We see that 2 \times 15 = 30 is the nearest. Now subtract 30 from 32 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{15)}02\phantom{5}\\15\overline{)320}\\\phantom{15)}\underline{\phantom{}30\phantom{9}}\\\phantom{15)9}20\\\end{array}
Use the 3^{rd} digit 0 from dividend 320
\begin{array}{l}\phantom{15)}021\phantom{6}\\15\overline{)320}\\\phantom{15)}\underline{\phantom{}30\phantom{9}}\\\phantom{15)9}20\\\phantom{15)}\underline{\phantom{9}15\phantom{}}\\\phantom{15)99}5\\\end{array}
Find closest multiple of 15 to 20. We see that 1 \times 15 = 15 is the nearest. Now subtract 15 from 20 to get reminder 5. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }5
Since 5 is less than 15, stop the division. The reminder is 5. 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}