Evaluate
27
Factor
3^{3}
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)972}\\\end{array}
Use the 1^{st} digit 9 from dividend 972
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)972}\\\end{array}
Since 9 is less than 36, use the next digit 7 from dividend 972 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)972}\\\end{array}
Use the 2^{nd} digit 7 from dividend 972
\begin{array}{l}\phantom{36)}02\phantom{4}\\36\overline{)972}\\\phantom{36)}\underline{\phantom{}72\phantom{9}}\\\phantom{36)}25\\\end{array}
Find closest multiple of 36 to 97. We see that 2 \times 36 = 72 is the nearest. Now subtract 72 from 97 to get reminder 25. Add 2 to quotient.
\begin{array}{l}\phantom{36)}02\phantom{5}\\36\overline{)972}\\\phantom{36)}\underline{\phantom{}72\phantom{9}}\\\phantom{36)}252\\\end{array}
Use the 3^{rd} digit 2 from dividend 972
\begin{array}{l}\phantom{36)}027\phantom{6}\\36\overline{)972}\\\phantom{36)}\underline{\phantom{}72\phantom{9}}\\\phantom{36)}252\\\phantom{36)}\underline{\phantom{}252\phantom{}}\\\phantom{36)999}0\\\end{array}
Find closest multiple of 36 to 252. We see that 7 \times 36 = 252 is the nearest. Now subtract 252 from 252 to get reminder 0. Add 7 to quotient.
\text{Quotient: }27 \text{Reminder: }0
Since 0 is less than 36, 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}