Evaluate
\frac{77}{51}\approx 1.509803922
Factor
\frac{7 \cdot 11}{3 \cdot 17} = 1\frac{26}{51} = 1.5098039215686274
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\begin{array}{l}\phantom{51)}\phantom{1}\\51\overline{)77}\\\end{array}
Use the 1^{st} digit 7 from dividend 77
\begin{array}{l}\phantom{51)}0\phantom{2}\\51\overline{)77}\\\end{array}
Since 7 is less than 51, use the next digit 7 from dividend 77 and add 0 to the quotient
\begin{array}{l}\phantom{51)}0\phantom{3}\\51\overline{)77}\\\end{array}
Use the 2^{nd} digit 7 from dividend 77
\begin{array}{l}\phantom{51)}01\phantom{4}\\51\overline{)77}\\\phantom{51)}\underline{\phantom{}51\phantom{}}\\\phantom{51)}26\\\end{array}
Find closest multiple of 51 to 77. We see that 1 \times 51 = 51 is the nearest. Now subtract 51 from 77 to get reminder 26. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }26
Since 26 is less than 51, stop the division. The reminder is 26. 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}