Evaluate
\frac{105}{13}\approx 8.076923077
Factor
\frac{3 \cdot 5 \cdot 7}{13} = 8\frac{1}{13} = 8.076923076923077
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)525}\\\end{array}
Use the 1^{st} digit 5 from dividend 525
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)525}\\\end{array}
Since 5 is less than 65, use the next digit 2 from dividend 525 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)525}\\\end{array}
Use the 2^{nd} digit 2 from dividend 525
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)525}\\\end{array}
Since 52 is less than 65, use the next digit 5 from dividend 525 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)525}\\\end{array}
Use the 3^{rd} digit 5 from dividend 525
\begin{array}{l}\phantom{65)}008\phantom{6}\\65\overline{)525}\\\phantom{65)}\underline{\phantom{}520\phantom{}}\\\phantom{65)99}5\\\end{array}
Find closest multiple of 65 to 525. We see that 8 \times 65 = 520 is the nearest. Now subtract 520 from 525 to get reminder 5. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }5
Since 5 is less than 65, stop the division. The reminder is 5. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}