Evaluate
\frac{554}{237}\approx 2.337552743
Factor
\frac{2 \cdot 277}{3 \cdot 79} = 2\frac{80}{237} = 2.3375527426160336
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\begin{array}{l}\phantom{2370)}\phantom{1}\\2370\overline{)5540}\\\end{array}
Use the 1^{st} digit 5 from dividend 5540
\begin{array}{l}\phantom{2370)}0\phantom{2}\\2370\overline{)5540}\\\end{array}
Since 5 is less than 2370, use the next digit 5 from dividend 5540 and add 0 to the quotient
\begin{array}{l}\phantom{2370)}0\phantom{3}\\2370\overline{)5540}\\\end{array}
Use the 2^{nd} digit 5 from dividend 5540
\begin{array}{l}\phantom{2370)}00\phantom{4}\\2370\overline{)5540}\\\end{array}
Since 55 is less than 2370, use the next digit 4 from dividend 5540 and add 0 to the quotient
\begin{array}{l}\phantom{2370)}00\phantom{5}\\2370\overline{)5540}\\\end{array}
Use the 3^{rd} digit 4 from dividend 5540
\begin{array}{l}\phantom{2370)}000\phantom{6}\\2370\overline{)5540}\\\end{array}
Since 554 is less than 2370, use the next digit 0 from dividend 5540 and add 0 to the quotient
\begin{array}{l}\phantom{2370)}000\phantom{7}\\2370\overline{)5540}\\\end{array}
Use the 4^{th} digit 0 from dividend 5540
\begin{array}{l}\phantom{2370)}0002\phantom{8}\\2370\overline{)5540}\\\phantom{2370)}\underline{\phantom{}4740\phantom{}}\\\phantom{2370)9}800\\\end{array}
Find closest multiple of 2370 to 5540. We see that 2 \times 2370 = 4740 is the nearest. Now subtract 4740 from 5540 to get reminder 800. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }800
Since 800 is less than 2370, stop the division. The reminder is 800. The topmost line 0002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}