Evaluate
\frac{64}{15}\approx 4.266666667
Factor
\frac{2 ^ {6}}{3 \cdot 5} = 4\frac{4}{15} = 4.266666666666667
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)192}\\\end{array}
Use the 1^{st} digit 1 from dividend 192
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)192}\\\end{array}
Since 1 is less than 45, use the next digit 9 from dividend 192 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)192}\\\end{array}
Use the 2^{nd} digit 9 from dividend 192
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)192}\\\end{array}
Since 19 is less than 45, use the next digit 2 from dividend 192 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)192}\\\end{array}
Use the 3^{rd} digit 2 from dividend 192
\begin{array}{l}\phantom{45)}004\phantom{6}\\45\overline{)192}\\\phantom{45)}\underline{\phantom{}180\phantom{}}\\\phantom{45)9}12\\\end{array}
Find closest multiple of 45 to 192. We see that 4 \times 45 = 180 is the nearest. Now subtract 180 from 192 to get reminder 12. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }12
Since 12 is less than 45, stop the division. The reminder is 12. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}