Evaluate
\frac{205}{43}\approx 4.76744186
Factor
\frac{5 \cdot 41}{43} = 4\frac{33}{43} = 4.767441860465116
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\begin{array}{l}\phantom{43)}\phantom{1}\\43\overline{)205}\\\end{array}
Use the 1^{st} digit 2 from dividend 205
\begin{array}{l}\phantom{43)}0\phantom{2}\\43\overline{)205}\\\end{array}
Since 2 is less than 43, use the next digit 0 from dividend 205 and add 0 to the quotient
\begin{array}{l}\phantom{43)}0\phantom{3}\\43\overline{)205}\\\end{array}
Use the 2^{nd} digit 0 from dividend 205
\begin{array}{l}\phantom{43)}00\phantom{4}\\43\overline{)205}\\\end{array}
Since 20 is less than 43, use the next digit 5 from dividend 205 and add 0 to the quotient
\begin{array}{l}\phantom{43)}00\phantom{5}\\43\overline{)205}\\\end{array}
Use the 3^{rd} digit 5 from dividend 205
\begin{array}{l}\phantom{43)}004\phantom{6}\\43\overline{)205}\\\phantom{43)}\underline{\phantom{}172\phantom{}}\\\phantom{43)9}33\\\end{array}
Find closest multiple of 43 to 205. We see that 4 \times 43 = 172 is the nearest. Now subtract 172 from 205 to get reminder 33. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }33
Since 33 is less than 43, stop the division. The reminder is 33. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}