Evaluate
\frac{86}{45}\approx 1.911111111
Factor
\frac{2 \cdot 43}{3 ^ {2} \cdot 5} = 1\frac{41}{45} = 1.9111111111111112
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)86}\\\end{array}
Use the 1^{st} digit 8 from dividend 86
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)86}\\\end{array}
Since 8 is less than 45, use the next digit 6 from dividend 86 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)86}\\\end{array}
Use the 2^{nd} digit 6 from dividend 86
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)86}\\\phantom{45)}\underline{\phantom{}45\phantom{}}\\\phantom{45)}41\\\end{array}
Find closest multiple of 45 to 86. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 86 to get reminder 41. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }41
Since 41 is less than 45, stop the division. The reminder is 41. 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}