Evaluate
27
Factor
3^{3}
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)945}\\\end{array}
Use the 1^{st} digit 9 from dividend 945
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)945}\\\end{array}
Since 9 is less than 35, use the next digit 4 from dividend 945 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)945}\\\end{array}
Use the 2^{nd} digit 4 from dividend 945
\begin{array}{l}\phantom{35)}02\phantom{4}\\35\overline{)945}\\\phantom{35)}\underline{\phantom{}70\phantom{9}}\\\phantom{35)}24\\\end{array}
Find closest multiple of 35 to 94. We see that 2 \times 35 = 70 is the nearest. Now subtract 70 from 94 to get reminder 24. Add 2 to quotient.
\begin{array}{l}\phantom{35)}02\phantom{5}\\35\overline{)945}\\\phantom{35)}\underline{\phantom{}70\phantom{9}}\\\phantom{35)}245\\\end{array}
Use the 3^{rd} digit 5 from dividend 945
\begin{array}{l}\phantom{35)}027\phantom{6}\\35\overline{)945}\\\phantom{35)}\underline{\phantom{}70\phantom{9}}\\\phantom{35)}245\\\phantom{35)}\underline{\phantom{}245\phantom{}}\\\phantom{35)999}0\\\end{array}
Find closest multiple of 35 to 245. We see that 7 \times 35 = 245 is the nearest. Now subtract 245 from 245 to get reminder 0. Add 7 to quotient.
\text{Quotient: }27 \text{Reminder: }0
Since 0 is less than 35, 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}