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\lceil -\frac{3}{5}-\frac{5}{5}\rceil +2
Convert 1 to fraction \frac{5}{5}.
\lceil \frac{-3-5}{5}\rceil +2
Since -\frac{3}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.
\lceil -\frac{8}{5}\rceil +2
Subtract 5 from -3 to get -8.
\lceil -2+\frac{2}{5}\rceil +2
Dividing -8 by 5 gives -2 and remainder 2. Rewrite -\frac{8}{5} as -2+\frac{2}{5}.
-1+2
The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of -2+\frac{2}{5} is -1.
1
Add -1 and 2 to get 1.
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}