Evaluate
\frac{614}{79}\approx 7.772151899
Factor
\frac{2 \cdot 307}{79} = 7\frac{61}{79} = 7.772151898734177
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\begin{array}{l}\phantom{79)}\phantom{1}\\79\overline{)614}\\\end{array}
Use the 1^{st} digit 6 from dividend 614
\begin{array}{l}\phantom{79)}0\phantom{2}\\79\overline{)614}\\\end{array}
Since 6 is less than 79, use the next digit 1 from dividend 614 and add 0 to the quotient
\begin{array}{l}\phantom{79)}0\phantom{3}\\79\overline{)614}\\\end{array}
Use the 2^{nd} digit 1 from dividend 614
\begin{array}{l}\phantom{79)}00\phantom{4}\\79\overline{)614}\\\end{array}
Since 61 is less than 79, use the next digit 4 from dividend 614 and add 0 to the quotient
\begin{array}{l}\phantom{79)}00\phantom{5}\\79\overline{)614}\\\end{array}
Use the 3^{rd} digit 4 from dividend 614
\begin{array}{l}\phantom{79)}007\phantom{6}\\79\overline{)614}\\\phantom{79)}\underline{\phantom{}553\phantom{}}\\\phantom{79)9}61\\\end{array}
Find closest multiple of 79 to 614. We see that 7 \times 79 = 553 is the nearest. Now subtract 553 from 614 to get reminder 61. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }61
Since 61 is less than 79, stop the division. The reminder is 61. 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}