Evaluate
\frac{1897}{555}\approx 3.418018018
Factor
\frac{7 \cdot 271}{3 \cdot 5 \cdot 37} = 3\frac{232}{555} = 3.418018018018018
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\begin{array}{l}\phantom{9990)}\phantom{1}\\9990\overline{)34146}\\\end{array}
Use the 1^{st} digit 3 from dividend 34146
\begin{array}{l}\phantom{9990)}0\phantom{2}\\9990\overline{)34146}\\\end{array}
Since 3 is less than 9990, use the next digit 4 from dividend 34146 and add 0 to the quotient
\begin{array}{l}\phantom{9990)}0\phantom{3}\\9990\overline{)34146}\\\end{array}
Use the 2^{nd} digit 4 from dividend 34146
\begin{array}{l}\phantom{9990)}00\phantom{4}\\9990\overline{)34146}\\\end{array}
Since 34 is less than 9990, use the next digit 1 from dividend 34146 and add 0 to the quotient
\begin{array}{l}\phantom{9990)}00\phantom{5}\\9990\overline{)34146}\\\end{array}
Use the 3^{rd} digit 1 from dividend 34146
\begin{array}{l}\phantom{9990)}000\phantom{6}\\9990\overline{)34146}\\\end{array}
Since 341 is less than 9990, use the next digit 4 from dividend 34146 and add 0 to the quotient
\begin{array}{l}\phantom{9990)}000\phantom{7}\\9990\overline{)34146}\\\end{array}
Use the 4^{th} digit 4 from dividend 34146
\begin{array}{l}\phantom{9990)}0000\phantom{8}\\9990\overline{)34146}\\\end{array}
Since 3414 is less than 9990, use the next digit 6 from dividend 34146 and add 0 to the quotient
\begin{array}{l}\phantom{9990)}0000\phantom{9}\\9990\overline{)34146}\\\end{array}
Use the 5^{th} digit 6 from dividend 34146
\begin{array}{l}\phantom{9990)}00003\phantom{10}\\9990\overline{)34146}\\\phantom{9990)}\underline{\phantom{}29970\phantom{}}\\\phantom{9990)9}4176\\\end{array}
Find closest multiple of 9990 to 34146. We see that 3 \times 9990 = 29970 is the nearest. Now subtract 29970 from 34146 to get reminder 4176. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }4176
Since 4176 is less than 9990, stop the division. The reminder is 4176. The topmost line 00003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}