Evaluate
\frac{3}{2}=1.5
Factor
\frac{3}{2} = 1\frac{1}{2} = 1.5
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\begin{array}{l}\phantom{5000)}\phantom{1}\\5000\overline{)7500}\\\end{array}
Use the 1^{st} digit 7 from dividend 7500
\begin{array}{l}\phantom{5000)}0\phantom{2}\\5000\overline{)7500}\\\end{array}
Since 7 is less than 5000, use the next digit 5 from dividend 7500 and add 0 to the quotient
\begin{array}{l}\phantom{5000)}0\phantom{3}\\5000\overline{)7500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 7500
\begin{array}{l}\phantom{5000)}00\phantom{4}\\5000\overline{)7500}\\\end{array}
Since 75 is less than 5000, use the next digit 0 from dividend 7500 and add 0 to the quotient
\begin{array}{l}\phantom{5000)}00\phantom{5}\\5000\overline{)7500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 7500
\begin{array}{l}\phantom{5000)}000\phantom{6}\\5000\overline{)7500}\\\end{array}
Since 750 is less than 5000, use the next digit 0 from dividend 7500 and add 0 to the quotient
\begin{array}{l}\phantom{5000)}000\phantom{7}\\5000\overline{)7500}\\\end{array}
Use the 4^{th} digit 0 from dividend 7500
\begin{array}{l}\phantom{5000)}0001\phantom{8}\\5000\overline{)7500}\\\phantom{5000)}\underline{\phantom{}5000\phantom{}}\\\phantom{5000)}2500\\\end{array}
Find closest multiple of 5000 to 7500. We see that 1 \times 5000 = 5000 is the nearest. Now subtract 5000 from 7500 to get reminder 2500. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }2500
Since 2500 is less than 5000, stop the division. The reminder is 2500. The topmost line 0001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}