Evaluate
\frac{90}{31}\approx 2.903225806
Factor
\frac{2 \cdot 3 ^ {2} \cdot 5}{31} = 2\frac{28}{31} = 2.903225806451613
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\begin{array}{l}\phantom{155)}\phantom{1}\\155\overline{)450}\\\end{array}
Use the 1^{st} digit 4 from dividend 450
\begin{array}{l}\phantom{155)}0\phantom{2}\\155\overline{)450}\\\end{array}
Since 4 is less than 155, use the next digit 5 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{155)}0\phantom{3}\\155\overline{)450}\\\end{array}
Use the 2^{nd} digit 5 from dividend 450
\begin{array}{l}\phantom{155)}00\phantom{4}\\155\overline{)450}\\\end{array}
Since 45 is less than 155, use the next digit 0 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{155)}00\phantom{5}\\155\overline{)450}\\\end{array}
Use the 3^{rd} digit 0 from dividend 450
\begin{array}{l}\phantom{155)}002\phantom{6}\\155\overline{)450}\\\phantom{155)}\underline{\phantom{}310\phantom{}}\\\phantom{155)}140\\\end{array}
Find closest multiple of 155 to 450. We see that 2 \times 155 = 310 is the nearest. Now subtract 310 from 450 to get reminder 140. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }140
Since 140 is less than 155, stop the division. The reminder is 140. The topmost line 002 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}