Evaluate
9
Factor
3^{2}
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)675}\\\end{array}
Use the 1^{st} digit 6 from dividend 675
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)675}\\\end{array}
Since 6 is less than 75, use the next digit 7 from dividend 675 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)675}\\\end{array}
Use the 2^{nd} digit 7 from dividend 675
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)675}\\\end{array}
Since 67 is less than 75, use the next digit 5 from dividend 675 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)675}\\\end{array}
Use the 3^{rd} digit 5 from dividend 675
\begin{array}{l}\phantom{75)}009\phantom{6}\\75\overline{)675}\\\phantom{75)}\underline{\phantom{}675\phantom{}}\\\phantom{75)999}0\\\end{array}
Find closest multiple of 75 to 675. We see that 9 \times 75 = 675 is the nearest. Now subtract 675 from 675 to get reminder 0. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }0
Since 0 is less than 75, stop the division. The reminder is 0. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}