Evaluate
\frac{100}{3}\approx 33.333333333
Factor
\frac{2 ^ {2} \cdot 5 ^ {2}}{3} = 33\frac{1}{3} = 33.333333333333336
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)500}\\\end{array}
Use the 1^{st} digit 5 from dividend 500
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)500}\\\end{array}
Since 5 is less than 15, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)500}\\\end{array}
Use the 2^{nd} digit 0 from dividend 500
\begin{array}{l}\phantom{15)}03\phantom{4}\\15\overline{)500}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}5\\\end{array}
Find closest multiple of 15 to 50. We see that 3 \times 15 = 45 is the nearest. Now subtract 45 from 50 to get reminder 5. Add 3 to quotient.
\begin{array}{l}\phantom{15)}03\phantom{5}\\15\overline{)500}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}50\\\end{array}
Use the 3^{rd} digit 0 from dividend 500
\begin{array}{l}\phantom{15)}033\phantom{6}\\15\overline{)500}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}50\\\phantom{15)}\underline{\phantom{9}45\phantom{}}\\\phantom{15)99}5\\\end{array}
Find closest multiple of 15 to 50. We see that 3 \times 15 = 45 is the nearest. Now subtract 45 from 50 to get reminder 5. Add 3 to quotient.
\text{Quotient: }33 \text{Reminder: }5
Since 5 is less than 15, stop the division. The reminder is 5. The topmost line 033 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 33.
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}