Evaluate
24
Factor
2^{3}\times 3
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)648}\\\end{array}
Use the 1^{st} digit 6 from dividend 648
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)648}\\\end{array}
Since 6 is less than 27, use the next digit 4 from dividend 648 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)648}\\\end{array}
Use the 2^{nd} digit 4 from dividend 648
\begin{array}{l}\phantom{27)}02\phantom{4}\\27\overline{)648}\\\phantom{27)}\underline{\phantom{}54\phantom{9}}\\\phantom{27)}10\\\end{array}
Find closest multiple of 27 to 64. We see that 2 \times 27 = 54 is the nearest. Now subtract 54 from 64 to get reminder 10. Add 2 to quotient.
\begin{array}{l}\phantom{27)}02\phantom{5}\\27\overline{)648}\\\phantom{27)}\underline{\phantom{}54\phantom{9}}\\\phantom{27)}108\\\end{array}
Use the 3^{rd} digit 8 from dividend 648
\begin{array}{l}\phantom{27)}024\phantom{6}\\27\overline{)648}\\\phantom{27)}\underline{\phantom{}54\phantom{9}}\\\phantom{27)}108\\\phantom{27)}\underline{\phantom{}108\phantom{}}\\\phantom{27)999}0\\\end{array}
Find closest multiple of 27 to 108. We see that 4 \times 27 = 108 is the nearest. Now subtract 108 from 108 to get reminder 0. Add 4 to quotient.
\text{Quotient: }24 \text{Reminder: }0
Since 0 is less than 27, stop the division. The reminder is 0. The topmost line 024 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 24.
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}