Evaluate
\frac{144}{43}\approx 3.348837209
Factor
\frac{2 ^ {4} \cdot 3 ^ {2}}{43} = 3\frac{15}{43} = 3.3488372093023258
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\begin{array}{l}\phantom{86)}\phantom{1}\\86\overline{)288}\\\end{array}
Use the 1^{st} digit 2 from dividend 288
\begin{array}{l}\phantom{86)}0\phantom{2}\\86\overline{)288}\\\end{array}
Since 2 is less than 86, use the next digit 8 from dividend 288 and add 0 to the quotient
\begin{array}{l}\phantom{86)}0\phantom{3}\\86\overline{)288}\\\end{array}
Use the 2^{nd} digit 8 from dividend 288
\begin{array}{l}\phantom{86)}00\phantom{4}\\86\overline{)288}\\\end{array}
Since 28 is less than 86, use the next digit 8 from dividend 288 and add 0 to the quotient
\begin{array}{l}\phantom{86)}00\phantom{5}\\86\overline{)288}\\\end{array}
Use the 3^{rd} digit 8 from dividend 288
\begin{array}{l}\phantom{86)}003\phantom{6}\\86\overline{)288}\\\phantom{86)}\underline{\phantom{}258\phantom{}}\\\phantom{86)9}30\\\end{array}
Find closest multiple of 86 to 288. We see that 3 \times 86 = 258 is the nearest. Now subtract 258 from 288 to get reminder 30. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }30
Since 30 is less than 86, stop the division. The reminder is 30. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}