Evaluate
\frac{122}{15}\approx 8.133333333
Factor
\frac{2 \cdot 61}{3 \cdot 5} = 8\frac{2}{15} = 8.133333333333333
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)122}\\\end{array}
Use the 1^{st} digit 1 from dividend 122
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)122}\\\end{array}
Since 1 is less than 15, use the next digit 2 from dividend 122 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)122}\\\end{array}
Use the 2^{nd} digit 2 from dividend 122
\begin{array}{l}\phantom{15)}00\phantom{4}\\15\overline{)122}\\\end{array}
Since 12 is less than 15, use the next digit 2 from dividend 122 and add 0 to the quotient
\begin{array}{l}\phantom{15)}00\phantom{5}\\15\overline{)122}\\\end{array}
Use the 3^{rd} digit 2 from dividend 122
\begin{array}{l}\phantom{15)}008\phantom{6}\\15\overline{)122}\\\phantom{15)}\underline{\phantom{}120\phantom{}}\\\phantom{15)99}2\\\end{array}
Find closest multiple of 15 to 122. We see that 8 \times 15 = 120 is the nearest. Now subtract 120 from 122 to get reminder 2. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }2
Since 2 is less than 15, stop the division. The reminder is 2. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}