Evaluate
75
Factor
3\times 5^{2}
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\begin{array}{l}\phantom{800)}\phantom{1}\\800\overline{)60000}\\\end{array}
Use the 1^{st} digit 6 from dividend 60000
\begin{array}{l}\phantom{800)}0\phantom{2}\\800\overline{)60000}\\\end{array}
Since 6 is less than 800, use the next digit 0 from dividend 60000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}0\phantom{3}\\800\overline{)60000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 60000
\begin{array}{l}\phantom{800)}00\phantom{4}\\800\overline{)60000}\\\end{array}
Since 60 is less than 800, use the next digit 0 from dividend 60000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}00\phantom{5}\\800\overline{)60000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 60000
\begin{array}{l}\phantom{800)}000\phantom{6}\\800\overline{)60000}\\\end{array}
Since 600 is less than 800, use the next digit 0 from dividend 60000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}000\phantom{7}\\800\overline{)60000}\\\end{array}
Use the 4^{th} digit 0 from dividend 60000
\begin{array}{l}\phantom{800)}0007\phantom{8}\\800\overline{)60000}\\\phantom{800)}\underline{\phantom{}5600\phantom{9}}\\\phantom{800)9}400\\\end{array}
Find closest multiple of 800 to 6000. We see that 7 \times 800 = 5600 is the nearest. Now subtract 5600 from 6000 to get reminder 400. Add 7 to quotient.
\begin{array}{l}\phantom{800)}0007\phantom{9}\\800\overline{)60000}\\\phantom{800)}\underline{\phantom{}5600\phantom{9}}\\\phantom{800)9}4000\\\end{array}
Use the 5^{th} digit 0 from dividend 60000
\begin{array}{l}\phantom{800)}00075\phantom{10}\\800\overline{)60000}\\\phantom{800)}\underline{\phantom{}5600\phantom{9}}\\\phantom{800)9}4000\\\phantom{800)}\underline{\phantom{9}4000\phantom{}}\\\phantom{800)99999}0\\\end{array}
Find closest multiple of 800 to 4000. We see that 5 \times 800 = 4000 is the nearest. Now subtract 4000 from 4000 to get reminder 0. Add 5 to quotient.
\text{Quotient: }75 \text{Reminder: }0
Since 0 is less than 800, stop the division. The reminder is 0. The topmost line 00075 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}