Evaluate
27
Factor
3^{3}
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\begin{array}{l}\phantom{24)}\phantom{1}\\24\overline{)648}\\\end{array}
Use the 1^{st} digit 6 from dividend 648
\begin{array}{l}\phantom{24)}0\phantom{2}\\24\overline{)648}\\\end{array}
Since 6 is less than 24, use the next digit 4 from dividend 648 and add 0 to the quotient
\begin{array}{l}\phantom{24)}0\phantom{3}\\24\overline{)648}\\\end{array}
Use the 2^{nd} digit 4 from dividend 648
\begin{array}{l}\phantom{24)}02\phantom{4}\\24\overline{)648}\\\phantom{24)}\underline{\phantom{}48\phantom{9}}\\\phantom{24)}16\\\end{array}
Find closest multiple of 24 to 64. We see that 2 \times 24 = 48 is the nearest. Now subtract 48 from 64 to get reminder 16. Add 2 to quotient.
\begin{array}{l}\phantom{24)}02\phantom{5}\\24\overline{)648}\\\phantom{24)}\underline{\phantom{}48\phantom{9}}\\\phantom{24)}168\\\end{array}
Use the 3^{rd} digit 8 from dividend 648
\begin{array}{l}\phantom{24)}027\phantom{6}\\24\overline{)648}\\\phantom{24)}\underline{\phantom{}48\phantom{9}}\\\phantom{24)}168\\\phantom{24)}\underline{\phantom{}168\phantom{}}\\\phantom{24)999}0\\\end{array}
Find closest multiple of 24 to 168. We see that 7 \times 24 = 168 is the nearest. Now subtract 168 from 168 to get reminder 0. Add 7 to quotient.
\text{Quotient: }27 \text{Reminder: }0
Since 0 is less than 24, stop the division. The reminder is 0. The topmost line 027 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 27.
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}