Evaluate
\frac{4500}{71}\approx 63.38028169
Factor
\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {3}}{71} = 63\frac{27}{71} = 63.38028169014085
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\begin{array}{l}\phantom{142)}\phantom{1}\\142\overline{)9000}\\\end{array}
Use the 1^{st} digit 9 from dividend 9000
\begin{array}{l}\phantom{142)}0\phantom{2}\\142\overline{)9000}\\\end{array}
Since 9 is less than 142, use the next digit 0 from dividend 9000 and add 0 to the quotient
\begin{array}{l}\phantom{142)}0\phantom{3}\\142\overline{)9000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 9000
\begin{array}{l}\phantom{142)}00\phantom{4}\\142\overline{)9000}\\\end{array}
Since 90 is less than 142, use the next digit 0 from dividend 9000 and add 0 to the quotient
\begin{array}{l}\phantom{142)}00\phantom{5}\\142\overline{)9000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 9000
\begin{array}{l}\phantom{142)}006\phantom{6}\\142\overline{)9000}\\\phantom{142)}\underline{\phantom{}852\phantom{9}}\\\phantom{142)9}48\\\end{array}
Find closest multiple of 142 to 900. We see that 6 \times 142 = 852 is the nearest. Now subtract 852 from 900 to get reminder 48. Add 6 to quotient.
\begin{array}{l}\phantom{142)}006\phantom{7}\\142\overline{)9000}\\\phantom{142)}\underline{\phantom{}852\phantom{9}}\\\phantom{142)9}480\\\end{array}
Use the 4^{th} digit 0 from dividend 9000
\begin{array}{l}\phantom{142)}0063\phantom{8}\\142\overline{)9000}\\\phantom{142)}\underline{\phantom{}852\phantom{9}}\\\phantom{142)9}480\\\phantom{142)}\underline{\phantom{9}426\phantom{}}\\\phantom{142)99}54\\\end{array}
Find closest multiple of 142 to 480. We see that 3 \times 142 = 426 is the nearest. Now subtract 426 from 480 to get reminder 54. Add 3 to quotient.
\text{Quotient: }63 \text{Reminder: }54
Since 54 is less than 142, stop the division. The reminder is 54. The topmost line 0063 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 63.
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}