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{77)}\phantom{1}\\77\overline{)88}\\\end{array}
Use the 1^{st} digit 8 from dividend 88
\begin{array}{l}\phantom{77)}0\phantom{2}\\77\overline{)88}\\\end{array}
Since 8 is less than 77, use the next digit 8 from dividend 88 and add 0 to the quotient
\begin{array}{l}\phantom{77)}0\phantom{3}\\77\overline{)88}\\\end{array}
Use the 2^{nd} digit 8 from dividend 88
\begin{array}{l}\phantom{77)}01\phantom{4}\\77\overline{)88}\\\phantom{77)}\underline{\phantom{}77\phantom{}}\\\phantom{77)}11\\\end{array}
Find closest multiple of 77 to 88. We see that 1 \times 77 = 77 is the nearest. Now subtract 77 from 88 to get reminder 11. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }11
Since 11 is less than 77, stop the division. The reminder is 11. 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}