Evaluate
\frac{507}{79}\approx 6.417721519
Factor
\frac{3 \cdot 13 ^ {2}}{79} = 6\frac{33}{79} = 6.417721518987341
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\begin{array}{l}\phantom{79)}\phantom{1}\\79\overline{)507}\\\end{array}
Use the 1^{st} digit 5 from dividend 507
\begin{array}{l}\phantom{79)}0\phantom{2}\\79\overline{)507}\\\end{array}
Since 5 is less than 79, use the next digit 0 from dividend 507 and add 0 to the quotient
\begin{array}{l}\phantom{79)}0\phantom{3}\\79\overline{)507}\\\end{array}
Use the 2^{nd} digit 0 from dividend 507
\begin{array}{l}\phantom{79)}00\phantom{4}\\79\overline{)507}\\\end{array}
Since 50 is less than 79, use the next digit 7 from dividend 507 and add 0 to the quotient
\begin{array}{l}\phantom{79)}00\phantom{5}\\79\overline{)507}\\\end{array}
Use the 3^{rd} digit 7 from dividend 507
\begin{array}{l}\phantom{79)}006\phantom{6}\\79\overline{)507}\\\phantom{79)}\underline{\phantom{}474\phantom{}}\\\phantom{79)9}33\\\end{array}
Find closest multiple of 79 to 507. We see that 6 \times 79 = 474 is the nearest. Now subtract 474 from 507 to get reminder 33. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }33
Since 33 is less than 79, stop the division. The reminder is 33. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}