Evaluate
\frac{8}{7}\approx 1.142857143
Factor
\frac{2 ^ {3}}{7} = 1\frac{1}{7} = 1.1428571428571428
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)80}\\\end{array}
Use the 1^{st} digit 8 from dividend 80
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)80}\\\end{array}
Since 8 is less than 70, use the next digit 0 from dividend 80 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)80}\\\end{array}
Use the 2^{nd} digit 0 from dividend 80
\begin{array}{l}\phantom{70)}01\phantom{4}\\70\overline{)80}\\\phantom{70)}\underline{\phantom{}70\phantom{}}\\\phantom{70)}10\\\end{array}
Find closest multiple of 70 to 80. We see that 1 \times 70 = 70 is the nearest. Now subtract 70 from 80 to get reminder 10. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }10
Since 10 is less than 70, stop the division. The reminder is 10. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}