Evaluate
45
Factor
3^{2}\times 5
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)540}\\\end{array}
Use the 1^{st} digit 5 from dividend 540
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)540}\\\end{array}
Since 5 is less than 12, use the next digit 4 from dividend 540 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)540}\\\end{array}
Use the 2^{nd} digit 4 from dividend 540
\begin{array}{l}\phantom{12)}04\phantom{4}\\12\overline{)540}\\\phantom{12)}\underline{\phantom{}48\phantom{9}}\\\phantom{12)9}6\\\end{array}
Find closest multiple of 12 to 54. We see that 4 \times 12 = 48 is the nearest. Now subtract 48 from 54 to get reminder 6. Add 4 to quotient.
\begin{array}{l}\phantom{12)}04\phantom{5}\\12\overline{)540}\\\phantom{12)}\underline{\phantom{}48\phantom{9}}\\\phantom{12)9}60\\\end{array}
Use the 3^{rd} digit 0 from dividend 540
\begin{array}{l}\phantom{12)}045\phantom{6}\\12\overline{)540}\\\phantom{12)}\underline{\phantom{}48\phantom{9}}\\\phantom{12)9}60\\\phantom{12)}\underline{\phantom{9}60\phantom{}}\\\phantom{12)999}0\\\end{array}
Find closest multiple of 12 to 60. We see that 5 \times 12 = 60 is the nearest. Now subtract 60 from 60 to get reminder 0. Add 5 to quotient.
\text{Quotient: }45 \text{Reminder: }0
Since 0 is less than 12, stop the division. The reminder is 0. The topmost line 045 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 45.
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}