Evaluate
\frac{244}{75}\approx 3.253333333
Factor
\frac{2 ^ {2} \cdot 61}{3 \cdot 5 ^ {2}} = 3\frac{19}{75} = 3.2533333333333334
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)244}\\\end{array}
Use the 1^{st} digit 2 from dividend 244
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)244}\\\end{array}
Since 2 is less than 75, use the next digit 4 from dividend 244 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)244}\\\end{array}
Use the 2^{nd} digit 4 from dividend 244
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)244}\\\end{array}
Since 24 is less than 75, use the next digit 4 from dividend 244 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)244}\\\end{array}
Use the 3^{rd} digit 4 from dividend 244
\begin{array}{l}\phantom{75)}003\phantom{6}\\75\overline{)244}\\\phantom{75)}\underline{\phantom{}225\phantom{}}\\\phantom{75)9}19\\\end{array}
Find closest multiple of 75 to 244. We see that 3 \times 75 = 225 is the nearest. Now subtract 225 from 244 to get reminder 19. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }19
Since 19 is less than 75, stop the division. The reminder is 19. The topmost line 003 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}