Evaluate
\frac{7}{2}=3.5
Factor
\frac{7}{2} = 3\frac{1}{2} = 3.5
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)630}\\\end{array}
Use the 1^{st} digit 6 from dividend 630
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)630}\\\end{array}
Since 6 is less than 180, use the next digit 3 from dividend 630 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)630}\\\end{array}
Use the 2^{nd} digit 3 from dividend 630
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)630}\\\end{array}
Since 63 is less than 180, use the next digit 0 from dividend 630 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)630}\\\end{array}
Use the 3^{rd} digit 0 from dividend 630
\begin{array}{l}\phantom{180)}003\phantom{6}\\180\overline{)630}\\\phantom{180)}\underline{\phantom{}540\phantom{}}\\\phantom{180)9}90\\\end{array}
Find closest multiple of 180 to 630. We see that 3 \times 180 = 540 is the nearest. Now subtract 540 from 630 to get reminder 90. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }90
Since 90 is less than 180, stop the division. The reminder is 90. 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}