Evaluate
15
Factor
3\times 5
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)825}\\\end{array}
Use the 1^{st} digit 8 from dividend 825
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)825}\\\end{array}
Since 8 is less than 55, use the next digit 2 from dividend 825 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)825}\\\end{array}
Use the 2^{nd} digit 2 from dividend 825
\begin{array}{l}\phantom{55)}01\phantom{4}\\55\overline{)825}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)}27\\\end{array}
Find closest multiple of 55 to 82. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 82 to get reminder 27. Add 1 to quotient.
\begin{array}{l}\phantom{55)}01\phantom{5}\\55\overline{)825}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)}275\\\end{array}
Use the 3^{rd} digit 5 from dividend 825
\begin{array}{l}\phantom{55)}015\phantom{6}\\55\overline{)825}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)}275\\\phantom{55)}\underline{\phantom{}275\phantom{}}\\\phantom{55)999}0\\\end{array}
Find closest multiple of 55 to 275. We see that 5 \times 55 = 275 is the nearest. Now subtract 275 from 275 to get reminder 0. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }0
Since 0 is less than 55, stop the division. The reminder is 0. The topmost line 015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}