Evaluate
\frac{75}{22}\approx 3.409090909
Factor
\frac{3 \cdot 5 ^ {2}}{2 \cdot 11} = 3\frac{9}{22} = 3.409090909090909
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\begin{array}{l}\phantom{220)}\phantom{1}\\220\overline{)750}\\\end{array}
Use the 1^{st} digit 7 from dividend 750
\begin{array}{l}\phantom{220)}0\phantom{2}\\220\overline{)750}\\\end{array}
Since 7 is less than 220, use the next digit 5 from dividend 750 and add 0 to the quotient
\begin{array}{l}\phantom{220)}0\phantom{3}\\220\overline{)750}\\\end{array}
Use the 2^{nd} digit 5 from dividend 750
\begin{array}{l}\phantom{220)}00\phantom{4}\\220\overline{)750}\\\end{array}
Since 75 is less than 220, use the next digit 0 from dividend 750 and add 0 to the quotient
\begin{array}{l}\phantom{220)}00\phantom{5}\\220\overline{)750}\\\end{array}
Use the 3^{rd} digit 0 from dividend 750
\begin{array}{l}\phantom{220)}003\phantom{6}\\220\overline{)750}\\\phantom{220)}\underline{\phantom{}660\phantom{}}\\\phantom{220)9}90\\\end{array}
Find closest multiple of 220 to 750. We see that 3 \times 220 = 660 is the nearest. Now subtract 660 from 750 to get reminder 90. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }90
Since 90 is less than 220, stop the division. The reminder is 90. 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}