Evaluate
75
Factor
3\times 5^{2}
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)1500}\\\end{array}
Use the 1^{st} digit 1 from dividend 1500
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)1500}\\\end{array}
Since 1 is less than 20, use the next digit 5 from dividend 1500 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)1500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1500
\begin{array}{l}\phantom{20)}00\phantom{4}\\20\overline{)1500}\\\end{array}
Since 15 is less than 20, use the next digit 0 from dividend 1500 and add 0 to the quotient
\begin{array}{l}\phantom{20)}00\phantom{5}\\20\overline{)1500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1500
\begin{array}{l}\phantom{20)}007\phantom{6}\\20\overline{)1500}\\\phantom{20)}\underline{\phantom{}140\phantom{9}}\\\phantom{20)9}10\\\end{array}
Find closest multiple of 20 to 150. We see that 7 \times 20 = 140 is the nearest. Now subtract 140 from 150 to get reminder 10. Add 7 to quotient.
\begin{array}{l}\phantom{20)}007\phantom{7}\\20\overline{)1500}\\\phantom{20)}\underline{\phantom{}140\phantom{9}}\\\phantom{20)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 1500
\begin{array}{l}\phantom{20)}0075\phantom{8}\\20\overline{)1500}\\\phantom{20)}\underline{\phantom{}140\phantom{9}}\\\phantom{20)9}100\\\phantom{20)}\underline{\phantom{9}100\phantom{}}\\\phantom{20)9999}0\\\end{array}
Find closest multiple of 20 to 100. We see that 5 \times 20 = 100 is the nearest. Now subtract 100 from 100 to get reminder 0. Add 5 to quotient.
\text{Quotient: }75 \text{Reminder: }0
Since 0 is less than 20, stop the division. The reminder is 0. The topmost line 0075 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 75.
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}