Evaluate
\frac{15}{2}=7.5
Factor
\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)165}\\\end{array}
Use the 1^{st} digit 1 from dividend 165
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)165}\\\end{array}
Since 1 is less than 22, use the next digit 6 from dividend 165 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)165}\\\end{array}
Use the 2^{nd} digit 6 from dividend 165
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)165}\\\end{array}
Since 16 is less than 22, use the next digit 5 from dividend 165 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)165}\\\end{array}
Use the 3^{rd} digit 5 from dividend 165
\begin{array}{l}\phantom{22)}007\phantom{6}\\22\overline{)165}\\\phantom{22)}\underline{\phantom{}154\phantom{}}\\\phantom{22)9}11\\\end{array}
Find closest multiple of 22 to 165. We see that 7 \times 22 = 154 is the nearest. Now subtract 154 from 165 to get reminder 11. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }11
Since 11 is less than 22, stop the division. The reminder is 11. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}