Evaluate
45
Factor
3^{2}\times 5
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)900}\\\end{array}
Use the 1^{st} digit 9 from dividend 900
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)900}\\\end{array}
Since 9 is less than 20, use the next digit 0 from dividend 900 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)900}\\\end{array}
Use the 2^{nd} digit 0 from dividend 900
\begin{array}{l}\phantom{20)}04\phantom{4}\\20\overline{)900}\\\phantom{20)}\underline{\phantom{}80\phantom{9}}\\\phantom{20)}10\\\end{array}
Find closest multiple of 20 to 90. We see that 4 \times 20 = 80 is the nearest. Now subtract 80 from 90 to get reminder 10. Add 4 to quotient.
\begin{array}{l}\phantom{20)}04\phantom{5}\\20\overline{)900}\\\phantom{20)}\underline{\phantom{}80\phantom{9}}\\\phantom{20)}100\\\end{array}
Use the 3^{rd} digit 0 from dividend 900
\begin{array}{l}\phantom{20)}045\phantom{6}\\20\overline{)900}\\\phantom{20)}\underline{\phantom{}80\phantom{9}}\\\phantom{20)}100\\\phantom{20)}\underline{\phantom{}100\phantom{}}\\\phantom{20)999}0\\\end{array}
Find closest multiple of 20 to 100. We see that 5 \times 20 = 100 is the nearest. Now subtract 100 from 100 to get reminder 0. Add 5 to quotient.
\text{Quotient: }45 \text{Reminder: }0
Since 0 is less than 20, 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}