Evaluate
\frac{81}{49}\approx 1.653061224
Factor
\frac{3 ^ {4}}{7 ^ {2}} = 1\frac{32}{49} = 1.653061224489796
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\begin{array}{l}\phantom{49)}\phantom{1}\\49\overline{)81}\\\end{array}
Use the 1^{st} digit 8 from dividend 81
\begin{array}{l}\phantom{49)}0\phantom{2}\\49\overline{)81}\\\end{array}
Since 8 is less than 49, use the next digit 1 from dividend 81 and add 0 to the quotient
\begin{array}{l}\phantom{49)}0\phantom{3}\\49\overline{)81}\\\end{array}
Use the 2^{nd} digit 1 from dividend 81
\begin{array}{l}\phantom{49)}01\phantom{4}\\49\overline{)81}\\\phantom{49)}\underline{\phantom{}49\phantom{}}\\\phantom{49)}32\\\end{array}
Find closest multiple of 49 to 81. We see that 1 \times 49 = 49 is the nearest. Now subtract 49 from 81 to get reminder 32. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }32
Since 32 is less than 49, stop the division. The reminder is 32. 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}