Evaluate
\frac{78}{53}\approx 1.471698113
Factor
\frac{2 \cdot 3 \cdot 13}{53} = 1\frac{25}{53} = 1.471698113207547
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\begin{array}{l}\phantom{53)}\phantom{1}\\53\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{53)}0\phantom{2}\\53\overline{)78}\\\end{array}
Since 7 is less than 53, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{53)}0\phantom{3}\\53\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{53)}01\phantom{4}\\53\overline{)78}\\\phantom{53)}\underline{\phantom{}53\phantom{}}\\\phantom{53)}25\\\end{array}
Find closest multiple of 53 to 78. We see that 1 \times 53 = 53 is the nearest. Now subtract 53 from 78 to get reminder 25. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }25
Since 25 is less than 53, stop the division. The reminder is 25. 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}