Evaluate
\frac{465}{61}\approx 7.62295082
Factor
\frac{3 \cdot 5 \cdot 31}{61} = 7\frac{38}{61} = 7.622950819672131
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\begin{array}{l}\phantom{61)}\phantom{1}\\61\overline{)465}\\\end{array}
Use the 1^{st} digit 4 from dividend 465
\begin{array}{l}\phantom{61)}0\phantom{2}\\61\overline{)465}\\\end{array}
Since 4 is less than 61, use the next digit 6 from dividend 465 and add 0 to the quotient
\begin{array}{l}\phantom{61)}0\phantom{3}\\61\overline{)465}\\\end{array}
Use the 2^{nd} digit 6 from dividend 465
\begin{array}{l}\phantom{61)}00\phantom{4}\\61\overline{)465}\\\end{array}
Since 46 is less than 61, use the next digit 5 from dividend 465 and add 0 to the quotient
\begin{array}{l}\phantom{61)}00\phantom{5}\\61\overline{)465}\\\end{array}
Use the 3^{rd} digit 5 from dividend 465
\begin{array}{l}\phantom{61)}007\phantom{6}\\61\overline{)465}\\\phantom{61)}\underline{\phantom{}427\phantom{}}\\\phantom{61)9}38\\\end{array}
Find closest multiple of 61 to 465. We see that 7 \times 61 = 427 is the nearest. Now subtract 427 from 465 to get reminder 38. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }38
Since 38 is less than 61, stop the division. The reminder is 38. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}