Evaluate
\frac{64}{61}\approx 1.049180328
Factor
\frac{2 ^ {6}}{61} = 1\frac{3}{61} = 1.0491803278688525
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\begin{array}{l}\phantom{61)}\phantom{1}\\61\overline{)64}\\\end{array}
Use the 1^{st} digit 6 from dividend 64
\begin{array}{l}\phantom{61)}0\phantom{2}\\61\overline{)64}\\\end{array}
Since 6 is less than 61, use the next digit 4 from dividend 64 and add 0 to the quotient
\begin{array}{l}\phantom{61)}0\phantom{3}\\61\overline{)64}\\\end{array}
Use the 2^{nd} digit 4 from dividend 64
\begin{array}{l}\phantom{61)}01\phantom{4}\\61\overline{)64}\\\phantom{61)}\underline{\phantom{}61\phantom{}}\\\phantom{61)9}3\\\end{array}
Find closest multiple of 61 to 64. We see that 1 \times 61 = 61 is the nearest. Now subtract 61 from 64 to get reminder 3. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }3
Since 3 is less than 61, stop the division. The reminder is 3. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}