Evaluate
\frac{49}{18}\approx 2.722222222
Factor
\frac{7 ^ {2}}{2 \cdot 3 ^ {2}} = 2\frac{13}{18} = 2.7222222222222223
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)98}\\\end{array}
Use the 1^{st} digit 9 from dividend 98
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)98}\\\end{array}
Since 9 is less than 36, use the next digit 8 from dividend 98 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)98}\\\end{array}
Use the 2^{nd} digit 8 from dividend 98
\begin{array}{l}\phantom{36)}02\phantom{4}\\36\overline{)98}\\\phantom{36)}\underline{\phantom{}72\phantom{}}\\\phantom{36)}26\\\end{array}
Find closest multiple of 36 to 98. We see that 2 \times 36 = 72 is the nearest. Now subtract 72 from 98 to get reminder 26. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }26
Since 26 is less than 36, stop the division. The reminder is 26. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}