Evaluate
\frac{40}{3}\approx 13.333333333
Factor
\frac{2 ^ {3} \cdot 5}{3} = 13\frac{1}{3} = 13.333333333333334
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\begin{array}{l}\phantom{7500)}\phantom{1}\\7500\overline{)100000}\\\end{array}
Use the 1^{st} digit 1 from dividend 100000
\begin{array}{l}\phantom{7500)}0\phantom{2}\\7500\overline{)100000}\\\end{array}
Since 1 is less than 7500, use the next digit 0 from dividend 100000 and add 0 to the quotient
\begin{array}{l}\phantom{7500)}0\phantom{3}\\7500\overline{)100000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 100000
\begin{array}{l}\phantom{7500)}00\phantom{4}\\7500\overline{)100000}\\\end{array}
Since 10 is less than 7500, use the next digit 0 from dividend 100000 and add 0 to the quotient
\begin{array}{l}\phantom{7500)}00\phantom{5}\\7500\overline{)100000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 100000
\begin{array}{l}\phantom{7500)}000\phantom{6}\\7500\overline{)100000}\\\end{array}
Since 100 is less than 7500, use the next digit 0 from dividend 100000 and add 0 to the quotient
\begin{array}{l}\phantom{7500)}000\phantom{7}\\7500\overline{)100000}\\\end{array}
Use the 4^{th} digit 0 from dividend 100000
\begin{array}{l}\phantom{7500)}0000\phantom{8}\\7500\overline{)100000}\\\end{array}
Since 1000 is less than 7500, use the next digit 0 from dividend 100000 and add 0 to the quotient
\begin{array}{l}\phantom{7500)}0000\phantom{9}\\7500\overline{)100000}\\\end{array}
Use the 5^{th} digit 0 from dividend 100000
\begin{array}{l}\phantom{7500)}00001\phantom{10}\\7500\overline{)100000}\\\phantom{7500)}\underline{\phantom{9}7500\phantom{9}}\\\phantom{7500)9}2500\\\end{array}
Find closest multiple of 7500 to 10000. We see that 1 \times 7500 = 7500 is the nearest. Now subtract 7500 from 10000 to get reminder 2500. Add 1 to quotient.
\begin{array}{l}\phantom{7500)}00001\phantom{11}\\7500\overline{)100000}\\\phantom{7500)}\underline{\phantom{9}7500\phantom{9}}\\\phantom{7500)9}25000\\\end{array}
Use the 6^{th} digit 0 from dividend 100000
\begin{array}{l}\phantom{7500)}000013\phantom{12}\\7500\overline{)100000}\\\phantom{7500)}\underline{\phantom{9}7500\phantom{9}}\\\phantom{7500)9}25000\\\phantom{7500)}\underline{\phantom{9}22500\phantom{}}\\\phantom{7500)99}2500\\\end{array}
Find closest multiple of 7500 to 25000. We see that 3 \times 7500 = 22500 is the nearest. Now subtract 22500 from 25000 to get reminder 2500. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }2500
Since 2500 is less than 7500, stop the division. The reminder is 2500. The topmost line 000013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}