Evaluate
\frac{15}{2}=7.5
Factor
\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5
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\begin{array}{l}\phantom{24)}\phantom{1}\\24\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{24)}0\phantom{2}\\24\overline{)180}\\\end{array}
Since 1 is less than 24, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{24)}0\phantom{3}\\24\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{24)}00\phantom{4}\\24\overline{)180}\\\end{array}
Since 18 is less than 24, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{24)}00\phantom{5}\\24\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{24)}007\phantom{6}\\24\overline{)180}\\\phantom{24)}\underline{\phantom{}168\phantom{}}\\\phantom{24)9}12\\\end{array}
Find closest multiple of 24 to 180. We see that 7 \times 24 = 168 is the nearest. Now subtract 168 from 180 to get reminder 12. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }12
Since 12 is less than 24, stop the division. The reminder is 12. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}