Evaluate
\frac{334}{41}\approx 8.146341463
Factor
\frac{2 \cdot 167}{41} = 8\frac{6}{41} = 8.146341463414634
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\begin{array}{l}\phantom{205)}\phantom{1}\\205\overline{)1670}\\\end{array}
Use the 1^{st} digit 1 from dividend 1670
\begin{array}{l}\phantom{205)}0\phantom{2}\\205\overline{)1670}\\\end{array}
Since 1 is less than 205, use the next digit 6 from dividend 1670 and add 0 to the quotient
\begin{array}{l}\phantom{205)}0\phantom{3}\\205\overline{)1670}\\\end{array}
Use the 2^{nd} digit 6 from dividend 1670
\begin{array}{l}\phantom{205)}00\phantom{4}\\205\overline{)1670}\\\end{array}
Since 16 is less than 205, use the next digit 7 from dividend 1670 and add 0 to the quotient
\begin{array}{l}\phantom{205)}00\phantom{5}\\205\overline{)1670}\\\end{array}
Use the 3^{rd} digit 7 from dividend 1670
\begin{array}{l}\phantom{205)}000\phantom{6}\\205\overline{)1670}\\\end{array}
Since 167 is less than 205, use the next digit 0 from dividend 1670 and add 0 to the quotient
\begin{array}{l}\phantom{205)}000\phantom{7}\\205\overline{)1670}\\\end{array}
Use the 4^{th} digit 0 from dividend 1670
\begin{array}{l}\phantom{205)}0008\phantom{8}\\205\overline{)1670}\\\phantom{205)}\underline{\phantom{}1640\phantom{}}\\\phantom{205)99}30\\\end{array}
Find closest multiple of 205 to 1670. We see that 8 \times 205 = 1640 is the nearest. Now subtract 1640 from 1670 to get reminder 30. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }30
Since 30 is less than 205, stop the division. The reminder is 30. The topmost line 0008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}