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{84)}\phantom{1}\\84\overline{)96}\\\end{array}
Use the 1^{st} digit 9 from dividend 96
\begin{array}{l}\phantom{84)}0\phantom{2}\\84\overline{)96}\\\end{array}
Since 9 is less than 84, use the next digit 6 from dividend 96 and add 0 to the quotient
\begin{array}{l}\phantom{84)}0\phantom{3}\\84\overline{)96}\\\end{array}
Use the 2^{nd} digit 6 from dividend 96
\begin{array}{l}\phantom{84)}01\phantom{4}\\84\overline{)96}\\\phantom{84)}\underline{\phantom{}84\phantom{}}\\\phantom{84)}12\\\end{array}
Find closest multiple of 84 to 96. We see that 1 \times 84 = 84 is the nearest. Now subtract 84 from 96 to get reminder 12. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }12
Since 12 is less than 84, stop the division. The reminder is 12. 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}