Evaluate
\frac{562}{69}\approx 8.144927536
Factor
\frac{2 \cdot 281}{3 \cdot 23} = 8\frac{10}{69} = 8.144927536231885
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\begin{array}{l}\phantom{69)}\phantom{1}\\69\overline{)562}\\\end{array}
Use the 1^{st} digit 5 from dividend 562
\begin{array}{l}\phantom{69)}0\phantom{2}\\69\overline{)562}\\\end{array}
Since 5 is less than 69, use the next digit 6 from dividend 562 and add 0 to the quotient
\begin{array}{l}\phantom{69)}0\phantom{3}\\69\overline{)562}\\\end{array}
Use the 2^{nd} digit 6 from dividend 562
\begin{array}{l}\phantom{69)}00\phantom{4}\\69\overline{)562}\\\end{array}
Since 56 is less than 69, use the next digit 2 from dividend 562 and add 0 to the quotient
\begin{array}{l}\phantom{69)}00\phantom{5}\\69\overline{)562}\\\end{array}
Use the 3^{rd} digit 2 from dividend 562
\begin{array}{l}\phantom{69)}008\phantom{6}\\69\overline{)562}\\\phantom{69)}\underline{\phantom{}552\phantom{}}\\\phantom{69)9}10\\\end{array}
Find closest multiple of 69 to 562. We see that 8 \times 69 = 552 is the nearest. Now subtract 552 from 562 to get reminder 10. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }10
Since 10 is less than 69, stop the division. The reminder is 10. 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}