Evaluate
\frac{18}{7}\approx 2.571428571
Factor
\frac{2 \cdot 3 ^ {2}}{7} = 2\frac{4}{7} = 2.5714285714285716
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\begin{array}{l}\phantom{140)}\phantom{1}\\140\overline{)360}\\\end{array}
Use the 1^{st} digit 3 from dividend 360
\begin{array}{l}\phantom{140)}0\phantom{2}\\140\overline{)360}\\\end{array}
Since 3 is less than 140, use the next digit 6 from dividend 360 and add 0 to the quotient
\begin{array}{l}\phantom{140)}0\phantom{3}\\140\overline{)360}\\\end{array}
Use the 2^{nd} digit 6 from dividend 360
\begin{array}{l}\phantom{140)}00\phantom{4}\\140\overline{)360}\\\end{array}
Since 36 is less than 140, use the next digit 0 from dividend 360 and add 0 to the quotient
\begin{array}{l}\phantom{140)}00\phantom{5}\\140\overline{)360}\\\end{array}
Use the 3^{rd} digit 0 from dividend 360
\begin{array}{l}\phantom{140)}002\phantom{6}\\140\overline{)360}\\\phantom{140)}\underline{\phantom{}280\phantom{}}\\\phantom{140)9}80\\\end{array}
Find closest multiple of 140 to 360. We see that 2 \times 140 = 280 is the nearest. Now subtract 280 from 360 to get reminder 80. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }80
Since 80 is less than 140, stop the division. The reminder is 80. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}