Evaluate
\frac{75}{11}\approx 6.818181818
Factor
\frac{3 \cdot 5 ^ {2}}{11} = 6\frac{9}{11} = 6.818181818181818
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)150}\\\end{array}
Use the 1^{st} digit 1 from dividend 150
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)150}\\\end{array}
Since 1 is less than 22, use the next digit 5 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)150}\\\end{array}
Use the 2^{nd} digit 5 from dividend 150
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)150}\\\end{array}
Since 15 is less than 22, use the next digit 0 from dividend 150 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)150}\\\end{array}
Use the 3^{rd} digit 0 from dividend 150
\begin{array}{l}\phantom{22)}006\phantom{6}\\22\overline{)150}\\\phantom{22)}\underline{\phantom{}132\phantom{}}\\\phantom{22)9}18\\\end{array}
Find closest multiple of 22 to 150. We see that 6 \times 22 = 132 is the nearest. Now subtract 132 from 150 to get reminder 18. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }18
Since 18 is less than 22, stop the division. The reminder is 18. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}