Evaluate
\frac{44}{15}\approx 2.933333333
Factor
\frac{2 ^ {2} \cdot 11}{3 \cdot 5} = 2\frac{14}{15} = 2.933333333333333
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)88}\\\end{array}
Use the 1^{st} digit 8 from dividend 88
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)88}\\\end{array}
Since 8 is less than 30, use the next digit 8 from dividend 88 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)88}\\\end{array}
Use the 2^{nd} digit 8 from dividend 88
\begin{array}{l}\phantom{30)}02\phantom{4}\\30\overline{)88}\\\phantom{30)}\underline{\phantom{}60\phantom{}}\\\phantom{30)}28\\\end{array}
Find closest multiple of 30 to 88. We see that 2 \times 30 = 60 is the nearest. Now subtract 60 from 88 to get reminder 28. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }28
Since 28 is less than 30, stop the division. The reminder is 28. 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}