Evaluate
\frac{85}{4}=21.25
Factor
\frac{5 \cdot 17}{2 ^ {2}} = 21\frac{1}{4} = 21.25
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\begin{array}{l}\phantom{400000)}\phantom{1}\\400000\overline{)8500000}\\\end{array}
Use the 1^{st} digit 8 from dividend 8500000
\begin{array}{l}\phantom{400000)}0\phantom{2}\\400000\overline{)8500000}\\\end{array}
Since 8 is less than 400000, use the next digit 5 from dividend 8500000 and add 0 to the quotient
\begin{array}{l}\phantom{400000)}0\phantom{3}\\400000\overline{)8500000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 8500000
\begin{array}{l}\phantom{400000)}00\phantom{4}\\400000\overline{)8500000}\\\end{array}
Since 85 is less than 400000, use the next digit 0 from dividend 8500000 and add 0 to the quotient
\begin{array}{l}\phantom{400000)}00\phantom{5}\\400000\overline{)8500000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 8500000
\begin{array}{l}\phantom{400000)}000\phantom{6}\\400000\overline{)8500000}\\\end{array}
Since 850 is less than 400000, use the next digit 0 from dividend 8500000 and add 0 to the quotient
\begin{array}{l}\phantom{400000)}000\phantom{7}\\400000\overline{)8500000}\\\end{array}
Use the 4^{th} digit 0 from dividend 8500000
\begin{array}{l}\phantom{400000)}0000\phantom{8}\\400000\overline{)8500000}\\\end{array}
Since 8500 is less than 400000, use the next digit 0 from dividend 8500000 and add 0 to the quotient
\begin{array}{l}\phantom{400000)}0000\phantom{9}\\400000\overline{)8500000}\\\end{array}
Use the 5^{th} digit 0 from dividend 8500000
\begin{array}{l}\phantom{400000)}00000\phantom{10}\\400000\overline{)8500000}\\\end{array}
Since 85000 is less than 400000, use the next digit 0 from dividend 8500000 and add 0 to the quotient
\begin{array}{l}\phantom{400000)}00000\phantom{11}\\400000\overline{)8500000}\\\end{array}
Use the 6^{th} digit 0 from dividend 8500000
\begin{array}{l}\phantom{400000)}000002\phantom{12}\\400000\overline{)8500000}\\\phantom{400000)}\underline{\phantom{}800000\phantom{9}}\\\phantom{400000)9}50000\\\end{array}
Find closest multiple of 400000 to 850000. We see that 2 \times 400000 = 800000 is the nearest. Now subtract 800000 from 850000 to get reminder 50000. Add 2 to quotient.
\begin{array}{l}\phantom{400000)}000002\phantom{13}\\400000\overline{)8500000}\\\phantom{400000)}\underline{\phantom{}800000\phantom{9}}\\\phantom{400000)9}500000\\\end{array}
Use the 7^{th} digit 0 from dividend 8500000
\begin{array}{l}\phantom{400000)}0000021\phantom{14}\\400000\overline{)8500000}\\\phantom{400000)}\underline{\phantom{}800000\phantom{9}}\\\phantom{400000)9}500000\\\phantom{400000)}\underline{\phantom{9}400000\phantom{}}\\\phantom{400000)9}100000\\\end{array}
Find closest multiple of 400000 to 500000. We see that 1 \times 400000 = 400000 is the nearest. Now subtract 400000 from 500000 to get reminder 100000. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }100000
Since 100000 is less than 400000, stop the division. The reminder is 100000. The topmost line 0000021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}