Evaluate
6
Factor
2\times 3
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)450}\\\end{array}
Use the 1^{st} digit 4 from dividend 450
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)450}\\\end{array}
Since 4 is less than 75, use the next digit 5 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)450}\\\end{array}
Use the 2^{nd} digit 5 from dividend 450
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)450}\\\end{array}
Since 45 is less than 75, use the next digit 0 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)450}\\\end{array}
Use the 3^{rd} digit 0 from dividend 450
\begin{array}{l}\phantom{75)}006\phantom{6}\\75\overline{)450}\\\phantom{75)}\underline{\phantom{}450\phantom{}}\\\phantom{75)999}0\\\end{array}
Find closest multiple of 75 to 450. We see that 6 \times 75 = 450 is the nearest. Now subtract 450 from 450 to get reminder 0. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }0
Since 0 is less than 75, stop the division. The reminder is 0. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}