Evaluate
\frac{91}{51}\approx 1.784313725
Factor
\frac{7 \cdot 13}{3 \cdot 17} = 1\frac{40}{51} = 1.7843137254901962
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\begin{array}{l}\phantom{51)}\phantom{1}\\51\overline{)91}\\\end{array}
Use the 1^{st} digit 9 from dividend 91
\begin{array}{l}\phantom{51)}0\phantom{2}\\51\overline{)91}\\\end{array}
Since 9 is less than 51, use the next digit 1 from dividend 91 and add 0 to the quotient
\begin{array}{l}\phantom{51)}0\phantom{3}\\51\overline{)91}\\\end{array}
Use the 2^{nd} digit 1 from dividend 91
\begin{array}{l}\phantom{51)}01\phantom{4}\\51\overline{)91}\\\phantom{51)}\underline{\phantom{}51\phantom{}}\\\phantom{51)}40\\\end{array}
Find closest multiple of 51 to 91. We see that 1 \times 51 = 51 is the nearest. Now subtract 51 from 91 to get reminder 40. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }40
Since 40 is less than 51, stop the division. The reminder is 40. 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}