Evaluate
\frac{913}{20}=45.65
Factor
\frac{11 \cdot 83}{2 ^ {2} \cdot 5} = 45\frac{13}{20} = 45.65
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)4565}\\\end{array}
Use the 1^{st} digit 4 from dividend 4565
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)4565}\\\end{array}
Since 4 is less than 100, use the next digit 5 from dividend 4565 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)4565}\\\end{array}
Use the 2^{nd} digit 5 from dividend 4565
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)4565}\\\end{array}
Since 45 is less than 100, use the next digit 6 from dividend 4565 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)4565}\\\end{array}
Use the 3^{rd} digit 6 from dividend 4565
\begin{array}{l}\phantom{100)}004\phantom{6}\\100\overline{)4565}\\\phantom{100)}\underline{\phantom{}400\phantom{9}}\\\phantom{100)9}56\\\end{array}
Find closest multiple of 100 to 456. We see that 4 \times 100 = 400 is the nearest. Now subtract 400 from 456 to get reminder 56. Add 4 to quotient.
\begin{array}{l}\phantom{100)}004\phantom{7}\\100\overline{)4565}\\\phantom{100)}\underline{\phantom{}400\phantom{9}}\\\phantom{100)9}565\\\end{array}
Use the 4^{th} digit 5 from dividend 4565
\begin{array}{l}\phantom{100)}0045\phantom{8}\\100\overline{)4565}\\\phantom{100)}\underline{\phantom{}400\phantom{9}}\\\phantom{100)9}565\\\phantom{100)}\underline{\phantom{9}500\phantom{}}\\\phantom{100)99}65\\\end{array}
Find closest multiple of 100 to 565. We see that 5 \times 100 = 500 is the nearest. Now subtract 500 from 565 to get reminder 65. Add 5 to quotient.
\text{Quotient: }45 \text{Reminder: }65
Since 65 is less than 100, stop the division. The reminder is 65. The topmost line 0045 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}